Peeling paint in a shower is from trapped moisture. Water from the shower or the roof gets behind the painted area and dampens the plaster. The moisture then pushes the bathroom paint off the plaster as it evaporates.
First, scrap off all the loose, peeling paint in the bathroom around the area to be patched. Wear a mask or a respirator while you are scraping (avoid sanding) due to the chance of lead in the paint. You can get a lead testing kit and check the surface for under $15. If there is lead paint present, you will want to here a professional to handle this repair.
After the loose paint is removed, clean the surface of the plaster. The moisture that caused the peeling may have left lime deposits on the surface of the plaster. To prevent these deposits from ruining the adhesion of our repair, wipe the area with warm water and a little bleach. Mix it six parts water to one part household bleach. Leave it on the surface for five minutes, and then rinse the area several times with clan warm water.
Once dry, prime the area with ZINSSER’S PEEL STOP. It will bond to the old paint and plaster forming a sound surface for the patching material.
To blend the peeling area to the bare plaster, use a six-inch putty knife to apply the drywall compound or spackling. Blending the painted area to the bare plaster will take several coats. Do not think you will save time piling thick layers of patching on the wall and sanding it off later.
Use two or three thin coats of patching compound and you will need very little sanding. This method requires less sanding and I hate that plaster dust, or at least my wife does.
A trick with using drywall compound is to smooth the edges with a damp sponge. Do not use the sponge where the patching is thick or wet; just smooth the edges where you are trying to blend in with the wall.
After the patch is sanded and smooth, tap a camp sponge with a little joint compound over the repaired area. This will emulate the texture of 30-years of paint and make your repair disappear.
Prime the repaired area with a latex primer.
To prevent mildew from reoccurring, use mildew proof paint or a mildew additive in your paint.