Hello, I use app-specific passwords for my email client. My app-specific password is not remembered despite asking it to be remembered. It works once and then asks again the next time around forcing me to create new app-specific passwords.
If you enter the password in account preferences, Claws Mail will remember it. If you do not enter it in account preferences, Claws Mail will ask for the password when it connects to the mail server, and offer to remember it only for current session, which means until you close Claws Mail. So if you want the password to be remembered permanently, open account preferences and enter it there.