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It is my experience that the internal parts of the inflator tend to corrode. There are replacement inflator valve assemblies on ebay for around $5 each that fit the DGX and many other inflators, and the DGX inflators themselves aren't that expensive. I carry a spare valve and the wrench.
Excellent idea, do you happen to have a pointer, my searches are coming up empty
If you don't have the service tool, try some vinegar and WD40 from out side but pushing the button, better from the inside you only need to take the hose apart