There is no indication in the Scriptures that he lost his privileges. In fact, he was later inspired to write two letters that became part of the Bible.
مِنَ ٱلْوَاضِحِ أَنَّ بُطْرُسَ تَوَاضَعَ وَقَبِلَ نَصِيحَةَ بُولُسَ .‏