So from what i understand the only way your gun rights are "gone forever" is if a court ordered you to go to a mental hospital. If it's just a 911 call and a ride to the hospital (every trip to the "grippy sock hotel" I've ever seen), that does not apply and your gun rights are not removed federally. Some states have "red flag" laws but to my understanding those are temporary and end either after a time period or a court petition. I'm curious what laws you're talking about in the US that would take your gun rights for a suicide call.
Involuntary commitment. Happened to a good friend of mine during a nasty divorce, the husband made up a suicidal story and my friend was committed without the court appointing her a lawyer to defend herself. She's struggling to get her rights back, it is apparently possible, but they're gone forever until you spend a lot of money on lawyers so it's true it's not strictly the case you can't get them back but they default to staying gone forever.
This heavily depends on the state.
E.g. NY is not friendly in this scenario depending on the type of permit and the type of hold. An involuntary hold will impact your right to have a gun.