I use thunderbird on desktop and bluemail on android smartphone.
Occasionally when sending or moving email(s) w\TB or BM the email(s) disappear. Usually if I then look in my account on the gmail website the email(s) will be there, but sometimes missing there too. Sometimes after being moved, the email(s) will be in one directory on website but another directory in TB and\or BM.
Sometimes several minutes or hours later the email(s) will reappear. Sometimes email(s) that disappear never reappear or might reappear in the original directory.
Other email(s) sent\moved later can be seen even though a previously disappeared email has yet to reappear.
Above sounds crazy, but ive been so meticulous to check every single time I send\move an email. Im completely sure of this. I 1st noticed this a very long time ago in TB shortly after I switched from pop3 to imap. This was before I had a smartphone. Back then I never checked the gmail website and just thought it was me. It has gotten slightly worse since I started using BM, prompting me to track every sent & moved email.
I can post the details of a specific incident.
Ive already asked in gmail/google forums.