Rather than a limit on the number of messages, Thunderbird may have problems if <i>Inbox</i> grows too big in size and/or, in the case of POP accounts, the file used to keep track of which messages have already been downloaded may develop problems as well. I would break that down into folders at the server using webmail and move smaller chunks into the server <i>Inbox</i>, so Thunderbird doesn't have to try to download it all at once. After each download, move the messages out of <i>Inbox</i> in Thunderbird, then compact the folder, to make room for the next chunk.