In account settings there is a setting in the synchronization and Storage for IMAP account that can limit the maximum message downloaded. This defaults to synchronize all messages regardless of age.

There is also a disk space heading in POP accounts which will allow you to limit the size of messages to download for POP accounts. This defaults to not selected.

Generally failure to download large email are the result of connection timeouts because an anti virus program of scanning the email and is simply too slow to do the job properly. Try disabling the anti virus mail scanner and see how that works for you. You will see discussions on extending the timeout values in Thunderbird to compensate for poorly written anti virus products, by my feeling is the products that would should be kept. Your system should not be slowed even further for the dubious value of mail scanning.

I'm using IMAP and don't have any limitations set. I've tried disabling the anti virus programs but that didn't help.

I installed Thunderbird on a different computer and added the email address for the particular message I'm having the problem with this time. When I opened the email message with an 8 jpg image attachment of 27MB, a big yellow banner opened saying Thunderbird blocked the remote content. It gave me about a dozen choices of what I wanted to do.

Naturally the choice I guessed was the wrong one so I got the same response, no download, as the other computer. (Had never seen the yellow banner on the other computer.) Uninstalling Thunderbird, reinstalling, and trying again didn't work at all. I've tried all the suggestions on the support page, youtube, reddit, etc. with no change. I've used Thunderbird for many years and it used to work great. This started happening awhile ago. Any large (3MB or larger) attached file especially pdf and jpg do not let me open or save them (but I have to wait for them to download). It's very aggravating. I've dealt with this too long, I'm going to delete Thunderbird from my computers and find another email client.