This isn't my area of expertise, though since there has been zero replies in three (one browser says August 9, another August 10 - probably something with time zones) days, here goes...
When in Airmail, either press Ctrl+M or tap the little envelope icon in the top left corner, to open the menu. Select either "Global settings" or "Settings" (because why should the menu be consistent between views...) and scroll down to "Debugging", which has a toggle for "Enable dubug logging". Unfortunately I don't know where the log ends up. I have, thus far, not found it. I think /System/Data/Data/com.gemini.airmail would seem likely. It is, however, not accessible without root, so I can't check. Perhaps some more GNU/Linux/Unix savvy member can add some details here?
When sending regular e-mail, one would typically use the SMTP server of the current internet provider. Quite often an ISP will only allow use of their own SMTP server, and may even block attempts to reach somebody else's, perhaps in an attempt to better control spam. This causes me some grief, as, when I'm connected to WiFi at home, the SMTP that works is different from when I'm on mobile data, but I can only configure one SMTP server per email account. Personally I've set it to the SMTP server of my mobile data provider, and will briefly turn off WiFi on my Gemini before sending e-mail, thus forcing mobile data to be used. Unless I knew what was going on, it would seem to me as if sending email would just sometimes fail (which is when I'm on WiFi). Could something similar be happening to you?
When a message fails to send, it ends up in the drafts folder of whatever account it was (attempted to be) sent from. Usually, I can open the message from there, and try to send it again, once I'm om the "correct" network.
Since I had to look more than twice to find the setting for outgoing server; enter into, say, the inbox of the account of interest, press Ctrl+M and select "Account settings". Note: even though "Account settings" shows up on the menu, when opened from the "Unified inbox", nothing will happen if you select it, probably since Airmail can't figure out which account you are trying to configure. Once the account settings are opened, scroll down to "Sending mail". The very last item, before the next section (which is "Folders"), is "Outgoing server". It's in a completely logical place, but I still found it hard to locate for some reason. In there, you can check the outgoing settings for your gmail account. Perhaps you can compare them to an account from which sending mail works and see if something is set up differently.
I have no idea if any of this is helpful at all, but it's the best I can do. If nothing else, keeping the thread a bit active might increase the chance that someone else, who might know more, might read and respond.