What you need is:

- Lepage Flexible Plastic Adhesive: http://www.lepageproducts.com/ProductDet...px?pid=130#
- artist paint brush
- glossy piece of any cardboard

if you have a large area fraying, use some low tack tape like plain white liner tape to cover the problem area first (which you may have done already but should redo fresh if you can).

-Squeeze some of this glue onto the cardboard
-dip the brush in it, picking up a good amount of glue
-quickly brush it over your problem area on the poly
-if you used some tape, make sure all the tape edges have been covered in glue to prevent it lifting any time later.

It doesn't take long for the glue to start skinning over so try to use very few brush stokes to maintain a smooth finish.

you can recoat after an hour or 2 if it needs it, but let it all cure for at least 24 hours before putting any tape over it.

I've used this for years recoat the poly bases of my old pieces.