I’m stumped as to why I’m having this problem.
I’m pasting my post from the Reaper forum here, just in case anyone has any advice…
Here’s what happens:

This is a test with a fresh install of both Reaper and TD - no MIDI communication between the two, no LoopMIDI, no Rearoute – both programs are in their ‘vanilla’ state. I’m using my Komplete 6 ASIO driver in Reaper (TD doesn’t have a driver ‘choice’, but rather sees everything in the system, and you then choose what to interact with via its nodes - since it’s really a programming environment much like Max). [I wonder if this has anything to do with the issue?]
So, in a nutshell: if TD is running (as in the program is running - doesn’t matter if it’s in ‘play’ or not), then Reaper’s playback freezes. the way to unfreeze it is to stop playback in TD, stop playback in Reaper, then start TD, then start Reaper… then the same things happens again.
I’ve tested against: Ableton, Bitwig, Audition and iZoptope RX10.
Interestingly, RX also freezes playback in a similar manner, whereas the other three are fine.
What to make of all this?!
I’m really interested to know if this is a problem specific to my system or whether anyone else can replicate the issue. If this is a ‘real’ problem, I’m amazed that nobody’s noticed… in fact, it would be impossible for anyone to actually use Reaper with TD, so I would have thought it would be a known issue… yet I see examples of people (well, at least one guy on youtube) happily working away with Reaper and TD.