His opening game saw Bury lose 1-0 to Portsmouth, while a goalless draw against Mansfield on Tuesday lifted the club to 20th in the League Two table.
However, despite the winless start, the club's board have opted to allow Jepson to remain as manager until 2014 in an effort to keep some stability.
"The main priority at this time is to implement a state of stability that can support the players to regain the type of form that we know they are capable of," read a statement on the club's official website.
"With this in mind and the fact that the players have demonstrated their full support for Ronnie Jepson, it has been decided to appoint Ronnie as the caretaker manager until January 2014. The current backroom team will also remain.
"This does allow the club to allow the dust to settle and assess the situation without being forced into any knee-jerk reactions."
Bury will face Wycombe Wanderers on Saturday.