It sounds like you're using auto-cron, which pulls tickets only when staff is active to trigger the request. It's kind of a last-ditch effort for getting emails into the system and isn't recommended if you can do otherwise.
You should set up an actual cron job if possible.
http://osticket.com/wiki/Email_Settings#POP3.2FIMAP_Polling(http://osticket.com/wiki/Email_Settings#POP3.2FIMAP_Polling)