Did Peter keep stumbling even after his earlier failures, and do believers ever stop stumbling?
The context records that this was not the first time Peter stumbled, and it states that believers do not reach a place where they never stumble. Peter remained human like everyone else; Paul publicly withstood him at Antioch because he was at fault.
Les teaches that sometime after the Jerusalem Council, Peter came to Antioch. Because these believers had been saved by the Gospel of Grace, they were free to eat whatever they wanted and were not under any dietary law. Paul withstood Peter to the face publicly because Peter was to be blamed. Les points out that this was not the first time Peter stumbled, nor do believers get to the place where they don't stumble. Peter was just as human as all of us; he stumbled, and Paul called him on it.