In this case all you need to do is securely reattach the top to the casework and you don't need to remove the entire top in order to do this. First, a few basics. The plastic laminate (Formica, Wilsonart, or another Brand laminate) is attached to the substrate, (either plywood or particle board), with an adhesive. The board complete with plastic laminate is then attached to the casework below with a construction adhesive and sometimes screws. In order for screws to work small blocks must first be installed level with the top of the casework as an anchor for the screws. In your case it sounds like your top was originally installed with glue only.

Since the top is only coming up in just a few places we suggest that you reattach it with a few dabs of construction adhesive. Look for something that comes in a tube that you can apply with a caulking gun. This will allow you to force the material into the joint between the underside of the top and the top edges of the casework. The most difficult part of this task will be working on your head in the casework below. The nice part is that it will go very quickly--just a couple of minutes.

Once you have applied an ample amount of adhesive place an abundance of books or other heavy objects on the top to weight it down to ensure a good bond at the glue joint. Leave the weight in place for about 24 hours in order to give the adhesive plenty of time to set up. Chances are your top will be good as new and will be ready to serve you for another 40 plus years!