An RCD controls all the circuits - it compares the curent between live and neutral and if there's a difference of (usually) 30mA then it trips out as a safety precaution - the assumption being that the "missing" current is passing through a person and may be electrocuting them.
From what you say it may be the fridge motor cutting in and out from time to time - I don't know fridge electrics well enough to hazard a guess beyond this - some motors have a motor start/run capacitor. Capacitors don't always last as long as you would wish - but not sure if fridge motors have caps...
RCDs often have an overload trip rating of 60+ Amps - your trip is more likely to be earth leakage than overload.
Good luck...
Peccavi
April 2010