I have a 10x12 or so flat roof on either end of the house. Always had
trouble with leaks and had to keep replacing the sheetrock ceilings.
One of the rooms extends the whole end of the house and is covered 1/2
by a pitched roof and 1/2 by the flat roof. The ceiling of the front
part (under the pitched roof) looks like 1x4's (3 1/4" exposed) butted
together, although it may be TIG.

I have replaced the flat roofs with rubber membrane systems and hope
to have no further trouble, but I am gun shy (especially since I'm
afraid the roof installation was not done correctly) and really do not
want to drywall these ceilings in case there is a leak down the road
and would appreciate alternative suggestions.

All suggestions appreciated!

JFM