when the app force close it reverts to the last saved state,
you dont lose training per se,
you just get what your training count is before the training spree that led to the crash.
lets say you have 60 full DP,
after training to 33 DP it crashes.
the game reverts to the save where you still have the 60 full DP.
Read more: http://digimonunlimited.proboards.com/thread/1145#ixzz2li6lLUN4