Beech, who arrived at Millmoor on a free transfer from Cardiff City in August 1998, has made just one start for the first team this season.
A statement on the club's official website said: "Beech has been unable to carve out a regular career despite the fact he has never let the team down whenever he has been called upon.
"He made a total of 40 league starts, plus 134 as a substitute. His one and only goal was one to remember, hitting the winner against Portsmouth last season."