Ultimately, ALL play modes will feature automated progress saving for the current level, mode, and game settings, ...but, I had a few days spare before I take a break with my family, so....
...I've nearly implemented PUZZLE MODE PROGRESS SAVING!
...complete with icons on the level previews to show those levels with games in progress/saved, if TetraLogical finds a save state for the previewed level and difficulty settings! (ie. Puzzle Mode, Hard, Level 14, etc)
So, when the update is released (hopefully tomorrow!) you'll find that exiting from an unfinished puzzle game will now create a save state/snapshot for it, then going back in to try that puzzle again will automatically reload it at the exact point where you left it!
ie. If you only have 5-10 minutes to play, you can still have a blast at progressing a particular level, then whenever you play a move, it will update the save state, ready to continue next time, if you have to exit the game.
If you want to take time to try and fully solve the CRAZY or HARD levels, for example, you can now take ALL the time you like, WHENEVER you like, figuring out the best moves, chipping away without needing to set aside a huge chunk of time to think about completing a tough puzzle in one go!
Enjoy guys! - Like I say, hopefully have it ready for release tomorrow!