could one be pop and the other IMAP? I know Google IMAP pushes new mail out when it arrives, so it might bypass the "new mail" process that occurs when Thunderbird checks for mail.

Thanks for trying but they are both configures as imap

right click the account, select settings. Select server settings Select advanced button untick Use IDLE comment and see if that causes a change.

both accounts are still configured the same

So they are both configures NOT to use IDLE, is that what you saying?

no. They are both configured to USE idle

well turn it off and see if that makes a change. After all IDLE is a server technology. If Google supports it and Yahoo does not then configuring Thunderbird the same means nothing. (I have no idea if Yahoo support it or not)

didn't work