Is it possible to save mid-level progress?
I have not played the game in some time but last time I did there was no save option, if you loaded the game up fresh you'd need to start from the beginning. That having been said on my android phone if I leave the game without closing it then it will suspend and when I go back it will resume in the state I left it (eg mid level). I suspect that can't be guaranteed to stay in that suspended state indefinitely though so while it might be good for short breaks I suspect it isn't practical as a long term "save" technique.
That having been said my experience is that once I've worked out the tricks for a levels the next time I go through it it is much quicker to get to a given point so you may find that having to replay half a level is not actually as bad as you are worried it might be.