That is a signal that the two are not equally set up. To resolve that, you need to investigate the two setups. Both need to be IMAP. You can do some detective work by logging on to your online account and send messages to yourself. Then, shut thunderbird off. Now, send a message to yourself and check if it's received on phone and whether it still shows online. If not, the phone appears to be POP and changing that will fix the issue. If the messages are still there, start thunderbird and see if it retrieves messages (although you can readily check that by clicking settings>account settings. Anyway, doing steps like that should help you resolve the disparity in setups.