Update: Didn't find a solution, but did get a couple of errors and weird glitches. One glitch I know was becuase of my graphics card, since it happens while playing Team Fortress 2 and many other games, but for the others I'm lost.
I tried it out once and on the third playthrough (not restarting, just clicking 'Play Again'), one of the spawn sprites moved to the middle of the screen where the player starts out at the start of the game... I have no idea why, but it's the same spawn sprite which always spawns an enemy first on the second playthrough (but that's not even happening anymore...). So I closed it and opened it again and that glitch with the spawn sprite relocating didn't happen, but when I got to my fourth playthrough this error appeared:
A crash inside the runtime has been intercepted! The crash may be a bug in Construct. Please report this to Scirra.
I'd love to report the bug but I'm not exactly sure what I'd be reporting
If it helps, I also got this error when trying to edit an event sheet (happens to several actually):
An invalid argument was encountered.
Well, I'll go cry in the corner now
EDIT: After realizing the game is taking longer to load on each playthrough I decided to take a time trial.
First playthrough: Immediately
Second: 18 seconds
Third: 40 seconds
Fourth: Didn't get it
Fifth: 2 minutes 32 seconds!
I think you're right Mipey, it does seem to be a memory issue.