A number of times I've started the game after quitting the game mid-tournament and either the option to continue wasn't there or continuing took me to a place much earlier in the last tournament.
Considering the game saves after every hand, this doesn't make much sense. Based on this, I should lose at most one hand (if I quit prior to it saving the currently hand). I shouldn't lose an entire tournament or entire portions of a tournament.
I've both benefited and been hurt by this. I was eliminated from a tournament and didn't get Ash's book. The game saved and everything so I quit. The next time I played, there was an option to continue the tournament which took me to the beginning of the tournament that I had lost (with Ash's book available). This time I won it.
I then played a few more tournaments. The last one I unlocked the final "bonus" objective and continued to play for a while (at least 5 or 6 hands, hence 5 or 6 saves) and then the game froze. When I went back in to play, the only option was to start a new tournament and the objective I completed was no longer completed (so I lost the entire last tournament).