I have got TheBat! connected to several accounts using Gmail as a mail server. On a particular account I am facing a strange issue as messages are considered as new one at a time. Therefore to get all messages I have to press F2 until all messages are downloaded.
I have got other account using Gmail and the same domain without any issue.
ISSUE SOLVED: It appears that email never were deleted on the server, I had more than 160'000 messages, I made some cleaning and reduce the number to about 12'000 and then mails are being downloaded fine.