Well, what’s happening is behind the touch pad is a membrane switch, made of Mylar Plastic, it’s really a Soft Touch Electric Conductive Material that when pressed the inner surface makes contact and it turns on, over time the conductive material wears out and gets stuck behind the housing that holds it in place.
To get it working again you’ll have to open up the Keypads, first UNPLUG the Microwave and remove the screws on both side and also the top and bottom, check that it’s in good condition, if not order a new Soft Touch KeyPad, if it is, use a mild cleaner, before you install it, make sure it’s DRY and clean, line up the keypad and housing, MAKE sure it’s lined up and the keypad can move up and down without getting stuck, put everything back and you should be ready to go!
Give it a good clean all round the button and maybe it will release it!
To begin with, what microwave button is sticking? If it is an actual button to release the door, clean it with John's suggestion-unplug it first. If it is a key pad, then it requires a more "internal" approach. It will depend on your level of skill and the availability of a new soft touch key pad, probably found at the manufacturer.
You might also try contacting the manufacturer, they have hot lines of service techs that can help you trouble shoot problems. Have the make and model numbers ready when you make the call.
Try cleaning it first, then maybe a spray of WD40 if it is still sticking.