But after avoiding relegation to League Two on the final day of the season, the club's seven-strong board of directors have unanimously decide to stick with Abbott.
Chief executive David Allen told the club's official website: "We want to bring continuity and stability to the club.
"We've had new owners in the last year and three new managers since June 2006. Now isn't the time for more changes.
"Now is the time for all of us to work together to put the disappointment of last season behind us and to move forward.
"Greg's in his first permanent post as a manager and he has a contract to take him through to the end of next season.
"We'll be doing everything we can to help him bring success to Carlisle United in that period."