Steven,

Easy fix - don't lose a moments sleep over this one. You have to take
out the threaded sleeve that the cover plate was attached to as Travis
says. Buy a new cover plate (preferably from the same manufacturer as
the original because they do have different thread pitches) and screw
it in.

Don't try to re-solder the cover plate because it is a special low
melting point alloy that is designed to fall off when heated.
Incinently you did the right thing removing the plate before painting
the ceiling. They don't work properly if you paint them.