seem to have same problem checked today for old BT order and noticed i haven't any emails further back than 18th january this year. i don't delete important emails and receipts and i should have emails going back a year or so if not longer. i hadn't notice this before and was trying to see if anyone else had issues. Dates seem to close to be different isuue. Not sure as what to do any advice would be helpfully
If you're accessing your emails on an email client (iPhone, Mac Mail, Outlook, etc..) you may have an option (specifically on apple products) to "Sync Mail" from a particular timeframe, eg: few days, 1 week, 2 weeks, 3 weeks, etc...
Have you tried accessing your emails through BT.com/mail or mail.yahoo.com (if BT YAHOO). This should hopefully narrow down where the issue lies.
Most likely the issue is a device configured for POP3 and not IMAP.