John:

T I have one screw that will stay in the ceiling metal register for a few
T months at a time, but it always falls out.
T
T How can I repair this so it has something to 'grab'? I have wrapped Teflon
T tape around the ridges of the screw to hopefully give it more surface area
T to attach to...

Using the next-larger screw may be a possiblity, as someone else
suggested, presuming the hole in the vent is sufficiently large. If
the screw screws into a metal flange there are U-shaped clips with a
threaded hole for bolts (not sure if this is the "Timmerman" thing
someone else suggested).

Depending on the scenario you might try those plastic 'mollies' ==
I'd only use them where it would expand against something solid, but
sheetrock is not solid: eventually a large hole will be created. The
metal mollies may work: the "wings" expand behind the sheetrock for
more surface area. Be sure to get the correct mollie for the drywall
thickness.

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