Re: Not sure what they used...
I would guess discrete flat-pack TTL (possibly of the LS variety) using exotic semiconductor materials that are less susceptible to radiation than normal silicon. Then ruggedized (conformal coating, plenty of 'bend' for interconnecting wires/cables, etc.), and LEADED solder [which does not form tin whiskers], thick circuit board material, lots of gold wiring where it matters, etc. etc. etc..
as an example (not sure if v*ger is using this) :
I bet it lasts a REALLY long time. How long before NASA sends a repeater satellite to follow it and relay its signals back/forth, for historical/legacy purposes?