I'm not sure if messages are missing or simply not appearing where expected. Your webmail appears to display in threaded view, whereas the TB view is unthreaded. I suggest setting webmail to unthreaded and comparing with TB. Sometimes threads are broken and messages appear outside of the thread.

Webmail is just an interface for reading emails on the server. Threading doesn't affect files. If it were just about marking messages as read/unread, this wouldn't be a problem. The problem is that TB doesn't see messages that are in the main inbox folder.

yes it is a interface, but to compare the two systems it is better to use the same interface on both. so change your Roundcube interface to non conversations and compare it to Thunderbird.