Train from Frankfurt to Amsterdam Schiphol Airport on time?

I guess it depends on if the train is on time

Correct. And "on time" is something you cannot depend on. Other things can happen as well (cancellations, closed sections of railway.) Unless you travel the day before and stay somewhere closer to Schiphol, you will be putting your flight home at some level of risk.

We only needed to get to Brussels from the Frankfurt airport. And we were on a high-speed train. The train had mechanical issues so what should have been 2.5 hours or so on the train turned into a 3+ hour ride because we disembarked, waited for a milk run, boarded, and then stood for the rest of the journey.

Your current schedule works just fine on paper, but what if...? When I plan our travel, I'm kind of a "belt AND suspenders" guy.

What is your cost - in time and money - if you miss the flight? If it's high on either or both, can you be there the night before? (We just got back from Amsterdam and there is loads to do there.) Can you take an earlier train and have lunch in Amsterdam? Can you live with checking your watch the entire train trip? Or...

Are you a "makuma matatta" traveler?

One of the things we enjoy about traveling is stumbling into something cool and unexpected when our plans fall apart...

Is this a flight home and in which country is home?

If you are flying to the US or Canada, keep this in mind.

If your train is late, and you miss your flight, the airline won't care. You were a no show. And unless you have a refundable ticket, you have just lost that ticket.

You will have to buy a new ticket. Not at the discounted rate but at the going rate that day.

Why not go to your airline's website and see what a last minute one way ticket will cost. Then ask yourself if you are okay with that.

If not, go to Amsterdam the day or night before and feel more confident you won't miss your flight.

When are you making this trip (date?). I ask because I can't find train connections with those times.

I also can't find a direct train to Schiphol from Frankfurt. It looks like you will have to change trains either at Amsterdam Centraal or Etrecht Centraal (faster). Fortunately, there are multiple trains per hour from either transfer station to Schiphol, so if your train is late getting to the transfer station, transferring shouldn't delay you much more.

Month and year of trip? Country of destination?

You didn't give every single detail, but we had an advance-purchase discount RAIL ticket on DB from Frankfurt that we didn't want to miss, and lose our money. But the S-Bahn we took from our hotel had a passed-out drunk on the floor, and the train did not depart. After 30 minutes, we called a taxi to get to the HBF!

The airline doesn't state conspicuously that you are to check in for an international flight 3-hours in advance just so they can skimp on gate agents (to save money), and make you wait an hour to get checked in for Economy seats.

They do it because the US Government requires them to provide a list of traveling passengers and their Passport (and other security-related) information some hours (not sure, maybe 6 hours) before the scheduled arrival time of the plane. Unless you are going Business class, I would not try to check in later than 3 hours before, measured from when you find the sign in the terminal that says "Flight XXX, Check-in Area ZZ3, Gates 253-262", and start looking for that.

Just for reference...I took maybe 4 or 5 longer trips by train in Germany, I think maybe one trip got me to my destination on time, the balance were a series of delays, missed connections, trouble on the tracks, you name it.

You do not mention if the flight is intra-Schengen or International, but at best it is cutting it close at less than a three hour window. That route also likely relies on a change or two, increasing your risk.

I would want more cushion to allow for any train delays. I've experienced them many times in many forms, including a rail strike that canceled my train to AMS altogether and I missed my flight. I would take an earlier train or make your way to Amsterdam the day before. You can check the projected crowds at the airport for your specific travel day about two weeks ahead, depending on the day and time of year the airport can be exceptionally busy: https://www.schiphol.nl/en/my-travel-day/today