As in the summary. Obvious downside is that the player can click past the prompt and be left with a "stuck" game. Still waiting for the space key but without any visible prompts.

Clicking should probably do nothing in this particular case.
Message should stay on top until the required action is performed.
The massage should have "press space to continue" somwhere in it.

This also applies to the death prompt.

Interestingly enough Y/n prompts are not subject to this and stay on top.