The 27-year-old started the first two matches of Paul Buckle's reign as manager, but he has since been left out of the match day squad for three games in succession.
He started the season on the transfer list, but forced his way back into the first team picture during Cheltenham's bright start to the season. He was sent off in the 1-0 home defeat by Southend United on September 16.
Taylor, who joined Cheltenham from Rotherham United in January 2013, has made 21 appearances this term and a total of 63 starts and 11 substitute appearances for the club, scoring three goals.
His contract expires at the end of the campaign.