"Ivan Gazidis said at the beginning of the season in one of the general meetings that we will never get rid of Arsene Wenger, he is here for life, although if the relationship with the supporters becomes so bad we might have to look at it again," Robson told talkSPORT.
"Well I think the relationship with supporters is getting worse. Their reaction to the [Alex Oxlade-Chamberlain] substitution wasn't just about that, it was because they are unhappy with how the season has gone so far.
"They're very frustrated that Arsenal aren't going to challenge for the league title this year and that substitution was the culmination of a lot of anger that has been vented towards Arsene Wenger in recent weeks."
The Gunners sit five points adrift of fourth-placed Chelsea.