I just updated the HeroMachine 3 alpha to A.20, which adds a cap of 20 actions to the number of undo levels. If that's not enough, let me know -- it's easy enough to change.
If you have more than 20 saved characters, I'd strongly encourage you to make a backup of your hmcharacters.sol file before you do too much today. This shouldn't impact the save file at all, but ... yeah, it makes me nervous, too. Better safe than sorry.
Hopefully this will stop the irritating Flash pop-up asking how much file space you want. Although, if you see that, just right-click on the HeroMachine app, choose "Settings" from the flyout, click the little folder icon, then set the file size to the next level up. 1MB usually works. You can check the "Don't bother me again" box if you want as well.
But like I said, hopefully this will stop it from being an issue at all.