After a poor run of form in the first half of last season, Everitt appeared to be under pressure before a late season upturn in performances and results took Edinburgh to the URC quarter-finals and the semi-finals of the Challenge Cup.
The South African’s contract expires at the end of the season and he confirmed he has yet to receive an offer of a new deal from Scottish Rugby.
Results in the next few months could determine Everitt’s future, but Brown believes Edinburgh’s problems run deeper than just the head coach.
“Edinburgh seem to be going between either a Richard Cockerill character, where they have to be shouted at and it’s very authoritarian all the time, or a Mike Blair or Sean Everitt character,” Brown, who started his career with Edinburgh before forging his reputation at Glasgow Warriors, said.
“It just seems like they can’t quite hit that sweet spot in the middle. At the same time, you can’t forget that’s a squad packed full of Scotland starters.
“Why is it that they can’t get results? They can get the one-off, the big results. We saw that in the run at the end of last season, getting into European play-offs, but they don’t seem to be able to get consistency throughout the week from game to game. I don’t think that’s just a coaching issue.
“We can’t just keep getting into that kind of cycle of new head coach, get rid of the head coach, new head coach, get rid of the head coach. There is something kind of systemic there.”