Barcham, 30, and Robinson, 35, both arrived from Portsmouth in 2015.
Former Tottenham trainee Barcham has netted six times in 32 appearances in all competitions this term, while former Millwall stalwart Robinson has appeared 39 times so far this season.
Defender Will Nightingale, 21, has also penned a new contract having made 10 appearances this campaign.
"It's a case of trying to make sure that we don't need major surgery in the summer," said Dons manager Neal Ardley.
AFC Wimbledon forward Andy Barcham and defender Paul Robinson have signed new, undisclosed-length deals with the club.