Reminds me:
Gradius, Zero Wing, and some other games:
In these games, you can power up your ship, and your ship gets gradually more powerful as you progress, but the enemies become more dangerous as well. The problem is, when you die, you lose all the power ups that you've obtained. This would be as if an RPG-ish game would, whenever you die, let you continue, but put you back at level 1 fighting monsters not meant for a level 1 character. Essentially, this means that either you beat the game in one life or you're not realistically going to beat the game at all. (Some later SHMUPs, like the Touhou series, made it so that you lose only some of your power on death, which is a lot more reasonable.)
Classic Castlevania games have a similar issue, but the issue tends to be not so much your power, but rather your subweapon. Die on stage 11 or 12 and you won't be able to get Holy Water before the stage 12 boss, which is nearly impossible to beat without it. There's also the problem of random subweapon drops; since you can only carry one subweapon, getting a random axe drop on stage 11 and you're screwed. (Fortunately, it seems that random subweapon drops only occur in CV1 and CV3; by the 16-bit era, Konami learned their lesson and got rid of random subweapon drops. With that said, I seem to remember one of the metroidcania CVs having an enemy with a subweapon drop.)