I’ve been catching up with the tower since I’ve been neglecting it for some time now and progressed through 20 something floors in a row. Then I’ve lost connection for split of a second and the game closed (cool design, huh). Guess what. Progress didn’t save. Turns out it saves only as you leave the tower (or die). Funny thing is, during that I’ve got achievement for doing 10 floors in a row, and it stayed.
Hope it’s not an intended mechanics of the game.
EDIT: Roster exp earned before “crash” stayed so it’s a way to farm infinite roster lvl. Better fix that fast before someone exploits that.