And no errors in logs ?
So as I understand - you have old mailbox with old messages and RC and other mail client can see this messages inside, but can't see new messages.
So it can be problem with your SMTP daemon or IMAP.
If another mail clients can't see just new messages and see another old - its not RoundCube problem.
When this problem starts ?
at first you must check your SMTP/IMAP logs, domain MX records.