Kittrick was appointed in January 2016 and led them to promotion to the EVO-STIK League Premier Division for the 2018/19 campaign.
The Seadogs made a strong start to the season and were top for several weeks, but lost their way around the Christmas period.
Bolder returned to the club before Christmas following his departure from North Ferriby United, but they now sit four points adrift of the play-off places.
The duo’s final game was a 2-1 home defeat to Stalybridge Celtic on Saturday which they led 1-0 through James Walshaw, only to concede two goals in the final three minutes to lose for the fourth time in their last seven games.
Play-off rivals Gainsborough Trinity have won four in a row since they dismissed Lee Sinnott, and they now sit in pole position for fifth place in the table.
The club say Steve Roberts will take charge of first team affairs at the Flamingo Land Stadium in the interim period with support from members of the current squad.
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