I am coming in late to this discussion. However, my thoughts are this:
In order to entirely strip someone of their right to possess a firearm, it is likely that some either judicial or administrative process will have to occur, with the right to appeal the decision either way. Right now, the individuals who are stripped of this right include: felons (obviously, they have been designated as felons through a judicial process) and the adjudicated mentally ill. The notion of "adjudicated mentally ill," in my state, means that someone has been through the involuntary commitment process and has been successfully committed by the State to a mental hospital. Merely being treated for depression or some other mental illness does not meet the definition.
So, two things would have to happen before your right is stripped: someone would have to file some sort of a petition alleging that your right should be stripped, and then there would be some burden of proof by which that allegation would have to be proved - probably by the proponent of the petition. Merely being treated, taking medications, etc., would, in my opinion, be inadequate to justify a decision to bar you from possession of firearms.
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