Because I've never had this problem befor upgrading to OXS 10.9, I see elsewhere that this may be a problem with this particular OSX because Apple made changes.  However, those references are generally about Apple Mail, not a 3rd party software like Outlook.  I also see that a fix is in the works for Apple Mail.  Because I see the same happening with Outlook, does this imply the problem is with how OSX handles email accounts, and that I'll have to wait for Apple? ... or can I expect a remedy from Microsoft?? (... whether it be a fix found here in this forum, or an software patch later)

EDIT:  My apologies ... the account I'm having problems with is my only POP account, which as it so happens cannot be configured as IMAP.  I'll need look into how its configured for deleting past emails ...

TA  (thanks anyway) :)