I used to have that problem with my Cruise Control as well – now it works perfectly, without a hitch! The solution was to resolder the CCA board. Many others have done this procedure with the same results.
The CCA seems to be another of those problem areas that everyone inevitably has to deal with after 10 or 15 years. Fortunately, like so many of the systems on this car, you can fix it yourself at minimal cost. In this case, 50 cents worth of solder and a couple of hours of your time.
When you pull the CCA and examine the board you’ll probably find that it looks ‘like new’, with no signs of burned components or broken traces. Nevertheless, what has likely happened is that one or more solder joints have loosened up due to deteriorative aging. The defect will Not be visible. You should systematically resolder each connection on the trace side of the board using the appropriate tools, solder and practices for electronic circuit boards. Then (using a magnifying glass) carefully inspect the board for solder bridges and remove them with desoldering braid.
I’ve done boards where I’ve also replaced the ICs, but this is usually to correct a total failure. Your symptoms suggest a deteriorated, intermittent solder joint. You could also replace your ICs (either 1 or 2) for about $1 while you’re at it.
After reinstalling the board in its case, you should also clean the external pins and apply a contact conditioner (available from computer and electronics shops).
Good luck, let me know if you have any questions.