The lyrics continues as this:
You say although we broke up
You still wanna be just friends
'Cause you don't really love me
You just keep me hangin' on
The singer complains that his partner does not love him anymore but she wants him to continue paying attention to her - to keep him hanging on.
It is obvious that the preposition on refers to the ...
You could easily use gather. Accumulate is a little bit more formal, but would also get the point across.
You might also want to think about using the verb to pool as in Pooled rain water will easily become a breeding ground for mosquitoes.