What could cause anterior discectomy with fusion c5-c6 to significantly protrude 3 months after surgery?

Not sure: A discectomy is just that, removal of the entire disc. So residual disc herniation should not occur, unless a complete discectomy was not performed for some reason.

Failure to fuse: It sounds as if the interbody spacer or bone graft failed to fuse and has displaced if this was a single level fusion done without instrumentation which can be done for one level surgery with typically no change in healing rate but a 10% chance of non union in a non smoker and higher risk in a smoker. Follow up with your surgeon as to next steps in treatment options.