I'm not sure what the record is more the longest unmoved piece, but Rupert Jones tipped me off about a game from the latest round of the 4NCL. David Eggleston kept his bishop on c1 for 51 moves. When it did move, it immediately got snapped of by his opponents knight. According to Rupert, it was constant position pressure from Simon Buckley that was responsible for the bishop immobility, pressure which eventually resulted in a winning ending.
Eggleston,David J (2367) - Buckley,Simon T (2347)
4NCL De Vere, Sunningdale, ENG (6.54), 12.02.2012