Thunderbird may or may not download all messages, depending on PC used.
Email - Gmail, POP OS: PC 1 & 2 - Windows 10 Pro
PC 3 - Windows 10 Home
Issue: On this one account, PC 1 downloads all messages as expected. PC 2 Generally downloads as expected PC 3 - May or may not download all messages. Typically will download only messages received in the last day. PC 3, during configuration, set itself up for windows mail to also access account. It downloads all messages.
I have compared configurations for the account on all 3 computers and have not detected a difference. PC 1 - Thunderbird has been around for several years (starting 2003) even though it is on it's 3rd computer. PC 2 - Thunderbird has been around for 4+ years PC 3 - Thunderbird has been on this system about 7 months.
All are running the latest version, whatever that might be.
Wšě wotmołwy (3)
The default for POP is to remove messages from the server. Check your settings if that is the case on any of your computers.
Typically IMAP is preferred when reading mail for the same account on different devices. https://support.mozilla.org/kb/imap-synchronization
Sorry it has taken so long. All devices are configured to leave mail on the server. I go in at the beginning of the year and delete old messages to avoid storage capacity issues.
I've been using email on multiple computers for over 15 years and never had a problem. The only change I am aware of, I'm now using Windows 10. There is the possibility that Google has done something. They do limit downloads to about 250 - 270 messages at a time. It is necessary for me to initiate the download several times when a lot of messages have built up.
It might be helpful to know how the status of a message on the server interacts with Thunderbird. i.e. How is it determined if a message is "New" or not. If there is some way to override this status condition and only download a message if it is NOT already on the particular PC doing the download.
Gmail and Pop being downloaded onto more than one computer.
In gmail webmail account via a browser, check settings as stated in 'Step 2: Set up POP'...see link below. 5. In the "POP download" section, what have you selected? select 'Enable POP for all mail' OR Enable POP for mail that arrives from now on. Suggest you choose the former not the latter.
Read this info regarding 'recent' mode...at link scroll down to the 'Troubleshooting' section.
https://support.google.com/mail/answer/7104828?hl=en
look at: 'I want to download emails on multiple email clients' If you need to use POP instead of IMAP, set up "Recent mode." Recent mode shows your last 30 days of emails from Gmail.