What is the proper method to prepare drywall for painting?
My bet is there's something in the old paint that's preventing good adhesion for the new paint. It's possible they used an oil-base indoors, or the paint had some chemical that messes with the latex you're likely using.

What I would do is buy an oil-based (mineral spirit cleanup) primer (like original Kilz) and prime the walls. Oil-based primers do a superb job of providing a "glue" layer for your latex to grab onto. Take a small area and test this hypothesis.

If that still fails, the next best thing is to put new drywall over the old and then paint fresh drywall. Obviously more expensive (and you'll need landlord permission), but you'd be guaranteed no paint problems.