Learn English – what’s the meaning of “for some time now”

In:

He has been working here for some time.

time as used here means one time of unspecified length, and does not refer to multiple times. So plural "times" would not be used.

As for sometimes, this is an abverb so you would not used it by itself in a prepositional phrase.
So you can't say:

He has been working here for sometimes.

but you can say:

He has been working here sometimes.

however the meaning here is various unspecified times, which is different from the original phrase, which meant one time of unspecified length.

It refers to the rate at which activities are filling up. People aren't signing up for the program and it's not just because it's a period where one might expect there to be a lower volume of signups- something's fundamentally wrong.