We booked a United flight (operated by Lufthansa) from Washington, DC to Istanbul with a 3.5 hour layover in Frankfurt but just received notice that a new departure time will only allow a 1 hour layover, a connection that will be impossible to make. There are 3 flights leaving Frankfurt later in the day for Istanbul. We are trying to decide whether to trust our luck that we can be rebooked onto one of these flights, or deposit the money we paid for the flight into our account and book a direct flight on Turkish Airlines with points.
Depends on your preferences.
A one-hour connection in Frankfurt is indeed tight, but it's also possible you could make the connection. And as you point out, if you misconnect, you have 3 more chances that day (I assume those are on Lufthansa?) so ultimately not a big deal.
While personally I'd much rather fly on Turkish Airlines than either United or Lufthansa, how are the cost comparisons?
How likely is it that you would be able actually use the credit with United before it expires?
If you would prefer flying on Turkish (I assume on a nonstop from Dulles to Istanbul), you might be able to just cancel your United booking for a refund, rather than for a credit for a future flight (I don't know that for sure but there's no risk in asking). If yes, then do so and go book the nonstop on Turkish (double check availability, price and other details to be sure first before you cancel your existing ticket).