Following the expiry of his previous loan deal at the weekend, Burke will now remain at the Coral Windows Stadium until 2 January 2016.
The defender briefly returned to West Ham for treatment on a recent knee injury but he will now rejoin up once again with Phil Parkinson's squad.
Parkinson said: "We are very pleased that Reece is remaining with us - we are going to need everyone over this busy Christmas period.
"Reece has been excellent for us, he is a very good player, but we just need to make sure we get his injury right first.
"It is important that we focus on this first but he is a good addition for us until January."