Apple Mail "Forgets" Password for Gmail

I've seen this problem documented elsewhere, but none of the "solutions" seem to work.

I have two-step verification enabled on my Gmail account. I generate a unique application password for Apple Mail, which I enter into the password field in the Mail application.

Inexplicably, anywhere from 5 minutes to 1 week later, when I attempt to send an e-mail I will be prompted that the password is "wrong." It isn't, because I HAVEN'T CHANGED ANYTHING. The only way I can get the message to go away is to revoke and then re-generate another unique password.

Interestingly, I can receive e-mails into the account with no problem, but it seems the sending part is where Mail gets wonky. I have tried:

-Removing the e-mail account entirely from Mail and setting it up from scratch

-Deleting all traces of the old password from my Mac, including from Keychain Access (did this combined with the above).

Any other suggestions? I am getting tired of this and am two steps from ditching Mail for a more functional e-mail client.