2002,Having intermittent problems with cruise control on my car

I am having problems with the cruise control on my car. When I try to engage it, the cruise control indication with stay on for a minute, and then it goes away. While that is happening, the cruise control on/off doesn't work or respond. After the minute is up, the indication goes off and then the cruise control will work. This happens about 25% of the time that I try to use cruise control. Any idea what could be causing this?