As this NGram shows, the single-word form is a relatively recent innovation...

If in doubt, put the space in. I can't think of any sentence where that would actually be considered incorrect by anyone. But as OP indicates, there are definitely contexts where most if not all native speakers would object to the single-word form.

I don't really think it makes much sense to claim different meanings for the two forms, but here's someone making a good stab at it.

As this NGram shows, the single-word form is a relatively recent innovation...

If in doubt, put the space in. I can't think of any sentence where that would actually be considered incorrect by anyone. But as OP indicates, there are definitely contexts where most if not all native speakers would object to the single-word form.

I don't really think it makes much sense to claim different meanings for the two forms, but here's someone making a good stab at it.

EDIT: (Many years later! :)

I just found this site, which says Anymore means at the present time, any longer, or from now on, whereas Any more means anything or something additional or further.

They also say Anymore is not normally considered an actual word in UK English, which explains my earlier position. But older and wiser, I can see the point of the distinction...

1:) I have enough staff. I don't need to hire anymore. (continued hiring is unnecessary)
2:) I have enough staff. I don't need to hire any more. (more staff are unnecessary)