Is there any specific pattern for those email which are not getting fetched sometimes?
(e.g. emails with attachments? from specific sender?)
-Also can you please check with Exchange Server's configuration.
You Can enable some debug logging also so that we have some more detailed logs.
How to enable email debug log is as ..BMC Remedy Various Logging.docx
Have a look at this KB.
you can see many KB on how to do basic checks for various tyrp of maiboxes like pop3,mapi,mbox..