I like the example. My position is if someone is deemed to be a current danger to society, they should be removed from it. If someone is not, then they should have all of their rights.
But to speak to your specific scenario, yes I think that person should be able to have a gun in the future. Just like I think someone who tries to OD on sleeping pills and booze, should not be banned from alcohol or sleeping pills in the future.
We actually do not have a provision to ban anyone from any other means of suicide, simply because they've attempted by those means. Not that I am aware of. The only thing we ban people from owning, if they've attempted suicide with it, would be a firearm (in certain jurisdictions that might find the person unsuitable thereafter). I think that is telling. It tells me that its less about preventing suicide and more about taking guns away from citizens.
I think if we want someone to be less-suicidal, taking their rights away permanently is probably a poor start toward that goal.