You actually DO lose your current progress if you don’t happen to save and happen to die on your last life. If you do happen to lose all your lives, you'll start back at where you last previously saved with four more lives added.
Yeah, it really sucks about that, but I recently found a couple of levels on the game I’m currently playing where you can stock up on a ton of extra lives really, really quickly. Super RMN World had a couple of levels like that as well, so I never really had to worry about that type of problem.
Oh, and speaking of exits at the start of a level, I just found a couple of levels that do that, actually. It’s quite a nice feature. I wish more levels did that.