Auto-cron means that emails are only fetched when an agent is active in osTicket, so my suggestion is to use normal cron instead as @[deleted] also asked for. For details see the email related topics in the wiki: osTicket.com/wiki
Regarding the issue itself, can you attach/post some more info about your email settings?
Does osTicket only fail to send the new ticket mails or does it fail to send mails at all?
Do you use SMTP or PHP mailer to send emails?