Yes, mail will disappear after certain days.
It says the duration in each mail. Usually, it's 3-day period.
Also, the items won't be expired if you put them in your inventory. So, claiming the items from the mailbox and leave them intact in your inventory won't make them expire.
The timer of the items will start running when you equip the items on your character.
You can try to send an RT via Contact Us if you wish.
Hopefully, they'll be able to return your items in that expired mail.