You may be hitting a locking problem that was recently reported and will be fixed in the next patch that we release.
To verify this, run this command when Paratext appears to be hung:
C:\Program Files (x86)\Paratext 9\ParatextForceShutdown.exe
This command will send in a report that usually allows us to see what is causing Paratext to hang.
John+Wickberg
Paratext Support