Thanks so much for your replies. We are trying to cut as many edges
without tape as we can. This was a very unusual situation where the
wall curved right into the ceiling. We are using the blue painters'
tape and taking it off right after the second coat has been applied.
We will use the removal trick mentioned.

Another factor that I realized--while it does not look like the plaster
walls have been painted before, the ceiling has. Might it be that the
ceiling was painted originally with an oil based paint, so the latex
would not stick? How could we tell that it is oil based? We would
prefer not to use oil-based paint while we're living here with our dog!