What kind of surface and what kind of paint? Do you mean flooring in or on a patio? You need to get back to a clean, solid surface first and foremost.
Don, without seeing a picture, it most likely was not applied to a properly prepared surface. Going forward, there is always the chance it will continue to peel in spots.
Meanwhile, scrape off everything loose and wash the entire surface. Concrete should be the roughness of 120 grit paper before it will adequately hold paint. If it is not sufficiently rough, you need to acid etch it.
When it is ready to paint, go to a paint store, like Sher-Wms. and buy their latex porch and deck paint. They can also give you valuable advice for your particular application.
If you used oil base patio paint, this is why it peeled, and you will need to prime it or sand it well before using the new latex.
This is the best answers I can give without knowing more specifics.
you nailed it even with my inadequate info. it is concrete but i can't srape it off....too big a job !any suggestions for taking the old paint up. btw i did buy it from SW but i don't recall what kind and i did etch the concrete with mratic acid but i suppose i applied it inadequately perhaps
If the surface was dusty, damp or unevenly etched, these could have led to failure. Additives such as Emulsabond can help in some marginally prepared conditions. Also, if the product was applied in full sun, it may not have had the drying time needed to soak in enough to get a good bite.
To fix it, In the perfect world the surface should be sandblasted clean.
A home grown option would be to get or make a pole scraper to remove the the bulk and then rent a large 3-4000psi pressure washer with an oscillating concrete cleaning tip and scour the surface of loose coating.