why do we need to study english?

Good:
Keep (it) alive.
Keep (it) cold.
Keep (it) quiet.
Keep (it) happy.
Keep (it) busy.
Keep (it) warm.
Keep (it) healthy.
Keep (it) empty.

Less good:
Keep (it) beautiful
Keep (it) rich.
Keep (it) sad.
Keep (it) free.
Keep (it) full.

So the primary qualification for the first list is "have I heard it before?" If I have and it seemed natural in context it gets an automatic pass.

Some of these sound better with the word "Stay" instead of "Keep' but it depends on the context. (example: "Keep (it) quiet" evokes more of a demanding image, but "Stay (no subject) quiet" sounds more like the speaker is also going to remain quiet.)

In general I think the rule is context. If a viable context for the phrase comes to mind, the phrase is much more likely to be placed in the "Good" column.

Maybe a secondary rule is "is it a noun?"
"Keep (it) beautiful" sounds powerfully Engrish to me. Maybe because it is a clear adjective? Whereas others (but by no means all) on the list are passable nouns. Of course the context rule supersedes that.

Empty vs Full - easier to keep something empty than to keep it full, hence easier context.
Happy vs Sad - difficult (or perhaps unpleasant) to conceptualize someone asking to keep something sad.

This is a fun excersize Schazer! Thanks!

Keep (it) real!