When paint doesn't do what paint is supposed to do - remove it all and start over with a good scrubbing.
In the past I've had great success with the use of acryllic water-based latex primer and paint. . . and I don't paint anything if it's going to be over 50% humidity outside. . . so that means nothing during the summer around here.
I'm a giiirl - The local hardware store is my shopping mall ;)