hold (one's) eyes open

To "hold your eyes open" means to stay awake, and to keep your eyes from closing:

Look at Jamie. He can't even hold his eyes open. Put him to bed.

This phrase is mostly used in negative sentences like the one above, where the speaker is saying that she can't hold her eyes open.

You could also say "keep your eyes open":

I can barely keep my eyes open.

This phrase appears in these lessons: