Sweet! To be a bit clearer about the saving issue, since you're looking into it:
I was using the downloaded Itch.io version. I booted up the game to play through some older levels to get enough bits for upgrades before before I tried to beat the second-to-last level. The first time I exited and continued, I suddenly had the same number of bits as when I'd continued from my last save file. Went "Argh!", played through some more levels, then exited once more and had the same problem. It seemed to fix itself the third time around, when I decided to just grind enough to actually purchase the upgrades I wanted before exiting the game—the upgrades and number of bits were the same the next time I continued from my file.
It's possible that the game just doesn't save your progress after you finish old levels? In which case, er, consider this general feedback on changing that.