Flight tickets came with an advisory of risky connection

Did you book it as a thru ticket on the United website or did you use a 3rd party Online travel agency?

Pam, Thank you, I forgot to mention that. Yes, I booked directly on United's website. I updated my post to reflect that too.

Flying all on one ticket? Then United is responsible for getting you to your destination if they sold you that ticket.

Is there a later flight the same day on to your destination? If so, United would try to get you on it. Is that just an hour or two later? Or not til the next day? In other words - what are you risking? Having to spend a night at an airport until you get the next flight the next day?

Did UAL say 'risky' or a 'close/tight' connection? Trying to alert you to make due haste and not dawdle between flights?

I'd call United customer service and see what other flight options they may have for a longer connection time. You can try researching other available flights for times first just to get an idea, but hopefully they can work something out for you. If you initially booked this flight with that 45-minute connection time, they may charge a fee to change it. Good luck!

If you booked this today, DOT rules say you have 24 hours to cancel the ticket for a full refund as you look for something less stressful.

How long until your trip? If you've got a couple of months, common advice is to hold the ticket for a couple of weeks and hope for a flight schedule change that would put you under what's known as an airline's minimum legal connection time. The general rule is that if the airline changes a schedule on you by more than 90-120 minutes OR puts a connection under the airline's internal MLCT for that routing, then you are allowed to either get the ticket refunded OR you get one free change to the ticket, including picking new flights with better connections or routings for you as long as you keep the same departure and arrival airports and, with a few exceptions, the same date as the original ticket.

Some light googling suggests that 40 minutes is United's minimum for domestic to international at Dulles so it wouldn't take much of a schedule tweak on their part to get you a free change to a better routing with more leeway for the connection.

A 45-minute connection is doable, but only if your first flight is not delayed. Now if you booked the entire trip as a single ticket with connections through United, then United is responsible for getting you onto the next available flight. That means you'll eventually arrive, just later than you'd planned.

As others have suggested, if you JUST booked the ticket, you have 24 hours to cancel your ticket without any cost penalties.

If not, then you can try calling United about an alternate flight. I would do my research before I called and explain that you want to change one leg of the flight from flight 9999 departing ABC airport on day of flight at 4:30 pm to flight 8888 departing ABC airport, same date, at 2:30 - or whatever options are available to you. Agents are often more accommodating if you can provide them a specific flight you want. There will probably be a change fee if you take this route, but that may be better for you than worrying about a tight connection.

I booked this directly with United as recommended by posters on another thread.
I know flying is a gamble but it seems the game is already rigged.

The posters say book directly with airline but that does not mean booking a flight with a 45 minute layover.
The airlines know they make money off budget travelers who know the rules, have a lot of flexibility and do not mind missing a connecting flight.

The posters say book directly with airline but that does not mean booking a flight with a 45 minute layover.

I think this is something we learn from traveling. At least, it's something I learned through experience. One assumes that if the airline sells the ticket, it must be okay. But once we've done a few international flights, we learn that a connection time depends on a lot of factors.

A 45-minute connection is doable, but only if your first flight is not
delayed. Now if you booked the entire trip as a single ticket with
connections through United, then United is responsible for getting you
onto the next available flight. That means you'll eventually arrive,
just later than you'd planned.

Keep in mind, if you miss your connection due to no fault of United's (weather, traffic, any force majeure etc), if there are no seats on the next flight to Ireland or the next flight is the following day, you will be paying for the hotel and meals. So outside of equipment failure or personnel issues, United won't be responsible for paying any costs for you waiting for the next available flight with seats.

Follow the advice given MANY times in this thread about changing your itinerary especially if you purchased this ticket within the last 24 hours.

We all learn from experience and I suspect you will never buy a ticket with such a short connection again either no matter if an airline 'allows' it. Airlines allow children under 2 years old to sit on adult's lap; but when there is severe turbulence, an adult's arms will do nothing to keep a child on his/her lap.

One assumes that if the airline sells the ticket, it must be okay.

I've made many cross-Atlantic trips, always booked directly though the airline, and always assumed that if they sold it, the connection must be OK. And it always has been, except once because of a major snow storm. But now I'm starting to see posts like this one, and it's clear that airlines are shrinking the connection times that they're willing to book. My last trip, this past April, originally had a connection in Munich that I thought might be a little tight, but when I found out that the next flight from Munich to my destination was only a few hours later, I didn't worry. I worried even less when the airlines made a schedule change that added 30 minutes to the connection time.

Thank you everyone for your replies.
Does anyone have any experience with flying the last flight of the day out of Dulles' Washington, DC airport?
I researched flights for my first leg to see what would get me to Dulles earlier. Apparently there are only 3 flights that day; the earliest will cause a 10 hour layover, the next a 5.5 hour layover and the one I've booked with the 45 minute layover. Not great options.
The 'risky connection' was a comment on the itinerary not during the booking of the flights.
My choice of flight gets me into Dublin at 10am. I like that timing because it gives me the day to adjust to the time difference and shops and businesses will be open.
I think I'm just being anxious.

"I think this is something we learn from traveling. At least, it's something I learned through experience. One assumes that if the airline sells the ticket, it must be okay. But once we've done a few international flights, we learn that a connection time depends on a lot of factors."

I agree with AquamarineSteph. Delta routinely sells a connection thru SLC with a 38 minute connection. I've made that several times both coming and going and have decided this stresses the heck out of me so I just won't accept that routing any more. Part of it is learning what YOU are comfortable with. I'm more willing to go with a short connection coming home than going.

As to your current choices, I'd take the 5.5 hour connection time if you can change without a penalty. Gives you leeway for a delayed flight from your departure airport.

Apparently there are only 3 flights that day; the earliest will cause
a 10 hour layover, the next a 5.5 hour layover and the one I've booked
with the 45 minute layover. Not great options.

I agree. Of those 3, choose the one with the 5.5 hour layover. You said you wanted to arrive at 10am and I would want that too.

If United is your only choice and an itinerary change comes with a $200+ change fee, then you may be better off leaving it "as is" and taking your chances because a hotel room (should you miss the flight) will likely cost you less than $200 if you pick the right one and you can minimize any other expenses (meals, etc.) in the worst case scenario if the airline will not reimburse you (that's unknown - although you should find put by reading the Terms of Carriage). But of course your vacation will start a day later and you'll have to calculate what that's worth to you. If you can change with no penalty, then that seems like the best bet (although you'll lose some vacation time, it won't be as many hours as if you miss the connection).

Whatever you do, make a decision and don't stress over it any more. If you're in the 24 hour purchase window, use it to your benefit. It's really not a big deal in the grand scheme of things because you will get to Ireland, but perhaps a little later than you thought. Or it could totally work out without any issue, and you'll be more careful about tight connections in the future if they cause you this much anguish.

After a long conversation with United representative, the only option I have is to cancel my entire reservation and book a new one with no guarantee of price. I have a few hours yet so I'll head back to the United website and search some more.
The good news is the typical flight last night was on time both legs. The 45 minute layover was as scheduled and no delays.
Thank you all for your replies.

If you're stuck with a long layover in Dulles, the Smithsonian aviation museum can be worth reclearing airport security to see:

https://airandspace.si.edu/udvar-hazy-center