No, there should not. 99.999% of the reasons why one might be in a mental health facility have zero bearing on that individual's RKBA.
The mental health issue is important, and certainly needs to be strengthened (just look at the recent lunatics who would have been prevented from mass-killings with reasonable adjustments to current policy and laws), but if we, as gun owners, keep banging on this mental health drum as if it's the source of all problems it's going to bite us in the arse.
As gun owners, we point with pride to the scientific studies which validate the benefits to society from our RKBA. We're clearly the side focused on truth, and that matters.
Well, use that same reverence for the truth when you talk about mental illness, because there's clear science showing that the *vast* majority of all mental health issues are not related to violence in any way. Failing to adhere to this will make us as bad as the antis...just spewing emotional crap.
So no generalized bans on the RKBA for mental health issues. Next thing you know, some quack with 2 years of junior college will decide you're stressed because of the heavy traffic during your commute, and therefore you lose all your guns? Not interested.