According to raw, it says that when a frenzy ends, the frenzied berserker is fatigued till the end of the encounter, the same as a rage does, and it says that you're exhausted when you add it to rage. Now it doesn't state anything special abou the duration of said exhaustion. Sure the berserker wouldn't be able to move for the rest of the encounter
, but nothing specifically states the fact that it should last longer than a couple of minutes. Nevertheless, I don't have my DMG or PHB here with me, so I'm not a 100% certain, since I really haven't read the rules on exhaustion and how long
it lasts..... Sorry, I just had this powerful urge to cover my ass.....
. But anyway, even if it does leave you exhausted for the day, I'd house rule it to a fatigued for the rest of the day, which is pretty harsh, but feasible, since the amount of adrenalin being pumped into the berserker's bloodstream must be in the order of 100's of cc's
... and you end up pretty tired after even a little adrenalin.