This sounds like failure to prepare the surface to be painted. You don't mention what the old surface (prior to applying the Alkyd paint) was, but unless that surface is aggressively sanded to break the surface glaze and then scrubbed with TSP and rinsed at least twice), there is a strong liklihood that new paint just wont stick. This is what I call the preparation/application inversion. That is, spending 10% of the time preparing the surface and 90% of the time applying the paint. It should be the other way around.
Now comes the tough part. You are going to have to scrape (vacuum??) off all the new paint off, getting back to the surface that needs preparation. And if done this way, you shouldn't require a primer, except for patch and repair spots.