Rustoleum paint wont work in a bike, correction.. it does work but u need at least 6 months for that paint to cure. THat the paint is dry to the touch doesnt men it is cure and sadly you choose a pretty bad paint for your project. So what is happening is not a surprise at all, always happens.
What u have to do is to paint the bike using urethane car paint. Is the only paint that will hold fine besides powder coating. Peel the paint to the bare metal.. clean it using mineral spirits... get 1 or 2 cans u-pol primer, i would use white or super light gray. Prime the bike with that, sand imperfections. Get 1/4 of a galon or a pint of urethane car paint, is called base coat-clear coat in the color u want. If you want a perfect match of the color u need probably your best bet is ppg paint. There is some cheapo car paint that will work but forget that you will get a perfect match of what u want, assuming you dont have a spray gun and stuff, ask the guys to put the paint in spray cans, 3 or 4 might do it fine. Paint that thing, sand the imperfections.
Now the clear coat, u have to get urethane clear coat, if you put something else the paint could crack after a few days. Get U-pol clear coat, 2 spray cans and spray it really nice, get a mask also because that thing is super toxic. Sand imperfections again, polish with paint polisher compound to get all super shiny. Done.