Alex,
Had the same cc problem with my '86 300E. Since I fixed it (about a year ago) it has worked flawlessly, so I must have done something right!
Actually there are 3 things worth doing:
1) remove the amplifier and carefully resolder all joints on the circuit board, as well as the connections to-and-from the board.
2) clean and oil (or light grease) the throttle linkage and joints.
3) clean and tighten the relevant ground connections in the cruise control circuit.

I did all 3 jobs at once, so I'm not sure what each of them contributed to solving the problem. The first, is probably essential; and the last two should be done anyway. You could always try the last-two first (they're the easiest), and if that doesn't work then pull the board.
Good luck, keep us posted.

Barrie