Some e-mails sent via EM Client, using Gmail via IMAP, do not show up in “Sent” or “All Mail” either, while they are clearly in the Sent folder inside Gmail (no other tags as all sent e-mails). Adding a tag in Gmail that should in theory make it show up in the proper folder does not help either. However, when trying to answer the e-mail from Gmail, creating a draft will allow both the draft and the original e-mail to show up in the Draft folder…
As the sent emails are not showing up in the Gmail IMAP Sent folder or All Mail folder but are showing in the Gmail sent folder online, then sounds like your local Gmail account has got out of sync with your online account.
To resync it, you can either run the repair option by “right clicking on your Gmail All Mail folder” and then and clicking “Properties” at the bottom. Then click the “Repair tab” at the top, and finally click Repair. The repair clears the local cache so emails will be slower to reread till fully cached again.
Or failing that “if the sent emails are still not showing in the Gmail Sent folder or All Mail folder”, then suggest to remove and readd your Gmail account via “Menu / Accounts” using the automatic account wizard at the top. That will also usually fix that issue if it’s corrupted in some way.
Alternatively the other option you can do to fix that is eg: If you have been making regular eM Client backups either automatically via the Settings or manually via “Menu / Backup”, then you could restore a recent dated backup when you know it was working ok via “Menu / File / Restore”, and then any new emails since the last backup will sync / update when eM Client connects.
Lastly once you get it working again, make a new manual backup via “Menu / Backup” incase you have any issues in the future. You can see when the manual backup is complete via clicking the dropdown arrow on the right of Refresh top left and clicking Show Operations. The backup goes in your “Documents / eM Client” folder by default.