what we call jails should essentially be mental hospitals, and the only people in them should be people that doctors have declared incapable of rehabilitating properly.
the purpose of a jail should be to protect society from people that can't be reformed, not to punish people for breaking the law.
so, should repeat gun offenders be jailed? well, if the system was working properly, it would catch these people before they're repeat offenders - because it would diagnose them properly, rather than waiting for them to misbehave.
it shouldn't be a question of how many times you've broken the law, but a question of whether you're able to understand what you're doing, or not.