How can i fix my push button cistern?

I have two push button toilets:
Two toilets.....two problems
1. One can only flush every 3/4 hours. what do i need to do to speed up the water coming in??
2. Not sure how to describe it! the little metal bit/bobble keeps popping out of the fitting and the toilet doesn't flush. If the bit/bobble is kept in (manually at the moment!) it works.