Purchasing German railroad point to point tickets on line

If it is on OBB, some of their trains do not open up until two weeks before the departure date.

OBB is the Austrian site, so not applicable.
I just did a dummy booking on bahn.de with no issues. What website were you using?
Since I don't know exactly what went wrong, perhaps have a look at this really useful site for all things train:
https://www.seat61.com/train-travel-in-germany.htm

I have the DB app & just tried for the end of December. No problem.

worked fine with me on the Bahn website - log in first
seat61.com is a great site to learn, but always buy on bahn.com

There is really not much reason to buy the tickets in advance. Except for Savings Fare tickets for a single traveler on an ICE/IC, full fare regional tickets will be cheaper and there is no price advantage to purchasing in advance. Just buy them for the same price at the station the day of travel or the day before if you are worried about getting them in time on the day of travel.

For regional travel, the least expensive way to get from Regensburg to Rothenburg is with a Bayern-Ticket, (always the same price, 34,-€ for 2P), and it is valid for any regional train(s) all day long (after 9am workdays).

Note: for some connections in early December, the connection includes a bus leg, and the Bahn website says "partial fare", but that would only apply to full fare regional tickets. If you had a full fare regional ticket, it would only include the trains indicated; you would have to pay extra for the bus. But the bus shown does accept Bayern-Tickets, so the cost of the Bayern-Ticket is the complete fare.

As Lee said, do it by Bayern Ticket - the pricing is especially advantageous if you are 2-5 persons traveling together.

http://munich-touristinfo.de/Bavaria-Ticket.htm

Because it's a day pass, you can use it for any detours within Bavaria that you choose to take, or for buses/trams/subway rides. You could make a stopover in Nuremberg if you like - drop your bags in a locker and spend a few hours seeing the old town, the Imperial Castle, or a WW II sight, or just having a meal. Any public transport you need during your stopover is covered. Then proceed to Rothenburg on whatever train gets you there at the desired hour. With the Bayern Ticket, you are not tied to any specific schedule.

Buy it at the station in Regensburg from a ticket machine on the day of travel - you get no price advantage by pre-purchasing.

you get no price advantage by pre-purchasing.

Not only that, but any Bayern-Ticket you purchase is for a specific date, so if you purchase it in advance, you can't later decide to use it on a different day. You have to purchase a new ticket for the different day.

I buy my Bayern-Ticket just before I jump on the train, or if I am concerned about taking the time to purchase it right before, I buy it the day before. We're not talking airline tickets here; buying a Bayern-Ticket is more like buying a bus ticket into town.

As people have said, just buy them from one of the many machines at the station. No need to buy them in advance for that type of train.