Your coat of arms is for your family, the title is for your character. So the two are separate in their function.
You can lose your title and regain it, or even get different titles elsewhere at higher or lower ranks throughout Elyria, but your coat of arms will just follow you where ever you go, as it's part of your family.
To "lose" your coat of arms you would have to marry into a different family and start using your new families coat of arms as your own.
Though this wouldn't "delete" your coat of arms, because even though you may leave your family, there would still be people in that family using your coat of arms.... so you may "regain" the coat of arms by marrying back into the family, or rejoining by some other method.
The only way for your coat of arms to be unattainable would be for everyone to officially leave your family. This would be because either everyone joined other family's via marriage/etc, or because everyone died and there isn't any heirs.
However depending how things play out, your coat of arms would still be ingame, you just wouldn't be able to access it as your own characters coat of arms. By this i mean that unless someone destroys EVERYTHING with your coat of arms on it, then it'll be ingame... like a book could have it in it, or a flag could have it on it, etc etc. It would be extremely unlikely that a coat of arms will ever be totally destroyed from the game..... doesn't mean you can't try thou :D
