There are a couple of problems that I think are compounding with each other. And I think a few small tweaks could really make a difference. Here's my (I'm not an authority on the subject so take it as you will) list in no particular order
1. Put some time in between death and restart. A short respawn is good for perma-death games like this but the current one is *too* short. For one it is a little jarring but more importantly sometimes when I die I don't know how I died not really giving me an opportunity to improve and leaving me with the impression that the game is unfair. This compounds with:
2. Remove the leaps of faith. There are at least two instances in the game where you have to jump onto a platform you cannot see. The game does a decent enough job telling me that I have to jump I just don't know to where. It feels unfair when I die to these since I couldn't see what I was supposed to be doing. This is made worse by the quick restart time since I don't get to see where I was supposed to land or even what I hit, meaning I just keep making the same mistakes over and over. I think these would be best simply removed from the game, but fixing 1 or making failure non-lethal would help.
3. Jump on space down. Currently if the space bar is down while you are on a platform you will jump. This means that if you land while holding the space bar from the last jump you will jump again immediately. This causes a good deal of deaths especially because holding space seems to make my jumps larger. If you only triggered the jumps when the player presses the space while already on the ground, then I wouldn't be jumping accidentally. You might want to also make it so that space presses just before landing (a few milliseconds or so) trigger a jump upon landing to be a little more forgiving to players, but holding space while landing should probably not initiate a new jump.
4. Be a little more forgiving with platform edges. A good deal of platformers will actually let you jump a little bit after you leave the edge of a platform. This prevents the player from thinking that the game just ignored their jump if they were a tiny bit late. It should be short enough that most players don't even notice that it is the case, but long enough that the players almost never feel like they should have jumped but didn't. There were definitely a few times where I felt certain I had jumped while on the edge of the platform but I had really been too late. Giving this tiny bit of leeway makes the game feel fairer and helps the player feel they are in control.
Criticisms aside I think the idea of the game is really neat. I like the way that once I reach the end of the game the game completely changes, and now I have to avoid enemies and pickups. I couldn't beat the game (I managed to avoid killing enemies and all of the pickups but the first [I honestly don't know how to avoid it]), but I thought that twist where I had to rethink everything was pretty neat.