Hello! Last year I used Liquid Nails to glue blue foam board insulation to a wooden door of an outdoor pump house. We get below zero temps here in winter. This spring the board all came off, the liquid nails just dried into a hard crust remaining on both surfaces, but not binding to each other. Any suggestions please?

Try Rhino glue. That stuff is tough and should hold through the extreme cold. Be careful not to get on your hands or fingers as youwill be stuck to yourself forever unless you use acetone to unglue yourself. It's like superglue on steroids.

Why not screw the foam to the wood? Use a galvanized deck screw that measures 1/4 to 1/2" more than the foam thickness.

If there is no heat source in the pump house that insulation does very little. Do the pipes ever freeze, is there power out there. PL 300 is cheap and works great. Henkel 1241199 pl-300 Foam Board Adhesive

Good Point ballenger, I suspect his pump house must be partially buried if it doesn't freeze up hard as a rock in sub zero temps. Heat tape? Liquid Nails is not compatible with foam and I don't think Rhino is either. There are other glues compatible with foam from the big box stores if you can't find the PL300. Read the labels. I would focus on Air sealing the door, and using screws as Ma641 suggests to hold the foam while the glue sets. I would use at least 2" of XPS at those temps and preferably 4".