Groves however has vowed that he's no quitter and he still believes he can turn the clubs fortunes around.
It is now nine games since Town's last win, the 3-1 away win at Brentford. Groves however refuses to walk away from the job.
"People who know me know I'm not a quitter," he told the Grimsby Telegraph.
"I think we can turn it around. Early on in the season we were more than capable of of playing against teams, dominating them and creating chances.
"Perhaps we didn't take the chances that we should have done in those games. But, from that point of view, I'm sure we can turn it around.
"But as each games goes by then it makes it difficult from a confidence point of view, and it needs to be done sooner rather than later.
"I'm the manager and and I'm responsible for it. If there's flak flying, then it's going to come at me.
"You're going to be low. It hurts. Your confidence can get affected and it means something."
Whilst Groves's determination to turn things round is admirable, the simple fact that he is failing was never clearer than now. If Groves won't walk away, the club must act and terminate his contract, for the sake of this club.