Byrne enjoyed a successful loan spell with the Shakers last term and put pen to paper on a two-year contract in August having been released by Leicester.
He made the last of four appearances during the current campaign in October's Johnstone's Paint Trophy penalty shoot-out triumph over local rivals Rochdale.
The 19-year-old has since endured a deeply frustrating period on the sidelines due to a blood infection.
"He's got that viral infection that we know about and he's just got to hope that we can get him through a month where he doesn't have a relapse," Blackwell explained. "Then, hopefully, that's the point that he can move on.
"There's no doubt we're looking at next season. This season's gone for Shane."