The 32-year-old missed the thrilling 3-3 draw with Oxford in the FA Cup on Saturday, and Stanley boss Leam Richardson fears he will be sidelined for a prolonged period.
"Bavs has been carrying a slight injury in the last few weeks and he got severely knocked on it on Tuesday night against Rotherham," Richardson told the club's official website.
"He had a scan and the results came through as him having torn ligaments and tendons in his shoulder. I think that potentially he could be out for the season."
The setback prompted Richardson to bring in Leeds keeper Paul Rachubka on an emergency loan, but with the deal lasting only a week, the 33-year-old is still weighing up a long-term solution.
"While the transfer window is closed I think you can only renew the seven days and then in January we'll look to do what we can to bring someone in," Richardson added.