Heat pressing might not fix anything, if it is peeling off, the screenprinter probably didn't use a nylon additive. You should be able to heat press it without damaging it, but you will need a vinyl made for nylon (thermoflex plus extra, siser extra, etc).

 

The wind shirt is probably nylon, When printing on Nylon you need an additive for the ink. More than likely this is the case from the ink lifting & no matter how many times you heat press it the ink fibers will not adhear to the nylon fabric

 

Nylon and plastisol aren't my forte, but I'm guessing that the original printer should have used an additive or specialist ink to encourage the plastisol to bond to the nylon, and didn't. If that is the case, re-pressing isn't likely to help.