Re glueing Kitchen Cabinet door laminate

The laminate/plastic covering on my Wickes kitchen cabinet doors is peeling away on the door edges. Anyone with a similar experience, what's a good glue to stick it back again, please?
It's not a separate edging strip, it's one piece moulded to the door; sheet of something, probably plastic - it's quite brittle.
I've tried superglue with some success. Of all things Poundland's 8 on a card seems to mostly work. Though not at a drop per inch! Trouble is it doesn't stick every one I've tried - about a 40% success rate. Branded superglue is far worse, of all things.
I'd rather use a proper glue that will stick all the peeling bits!

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