I haven't dealt with cruise controls for at least 10 years, but, since there are literally DOZENS of types, here goes my limited knowledge:
The "Resume" button is bad or dirty.
If mounted on the end of the T/S switch, it can even be the small wires that go from the T/S arm down the column.
If steering whel spoke mounted, clean the switch and the slip rings.
Some depend on specific resistance changes to operate, and dirty slip rings/brushes can do that.
Fuses. Some have 2 power feeds, unswitched battery and ignition.
Sometimes, some functions won't work if one supply is bad (but generally other things will not work at the same time).
If someone has done any electrical work of late, especially anything to do with aftermarket raio, IPods, handless cell phones, sometimes folks probe a wire looking for power and get what they think is what they want, and it's a load sensitive cruise control line.