Beer is 95% water. If you’re counting on it for all your calories, you probably won’t want to drink any additional water or you lose your precious salt and vitamins.

As others have noted vitamin C and salt are probably the most immediate lacking nutrients. If you had a margarita once a week, I think that might be enough.

Numerous people have done a 40-day fast for lent, taking only beer. So that is easily doable. Multiple months is probably possible, but seasons/years maybe not.