Have prefab cabinets and tried to paint them but paint won't stay on.

What primer did you use?

What type of paint did you use - latex, acrylic, alkaline, oil?

Were the cabinets cleaned well?

Sand them first. Q

Did you use a primer? I would strip the paint off, sand it a bit and prime before painting.

https://www.bobvila.com/articles/painting-laminate-cabinets/#.Wk5DRrenGpo

Was the cabinet panel cleaned and sanded first? Proper surface prep is important to a quality result. Additionally you might call customer service listed on your paint can. Paint companies are extremely helpful with customer support even supplying replacement product when a failure occurs on their part. I had the wood knot bleed through on a porch ceiling that as successfully resolved with corporate replacement product.

I have learned there are different primers. This Valspar primer which is thick, performed perfectly on our PVC laundry room pipes. It covered the shiny pipe, purple pvc cement stain and red lettering and allowed us to apply wall paint to make the pipes less visable.

Even though many paints now tout "paint and primer in one" each situation requires its own prep work depending on the surface to be painted.

Pre-fab = plastic, not solid wood based. There is the source of the problem.

how did you prep the cabinets?

Use a good degreaser To clean them. Rinse well. Use Zinser brand BIN shellac based primer. Let dry for 24 hours. You can then paint the cabinets with any paint you choose. We used Dutch Boy cabinet and trim paint from Menards and our cabinets look great and it held up beautifully.