Emails not pushing through

Along with my other problem (rotation not working) I have now no email coming through unless I sync peak midnight to midnight every 15 mins. It wasnt synced before and email was pushed in. I do not want to sync the accounts I have as it drains battery and also downloads lots of mail that I do not want from months ago.Have cleared cache, data and force stop.Why is my email not working? I do not intend doing a factory reset with all the work involved in setting up phone again (after 3 times its a pain) . I have tried removing email and adding them again and still not working.There is no refresh option for email and there is no clear cache option for email either.is there any way to go back to what I had before? I.e constant geting pushed through when an email arrives? OR- how can I get my email to work? Not willing to do factory reset just to see if it rectifies the problem. Lots of work setting it all up again with the amount of stuff ive had to re get.

Thanks

 

Its the s2 and im not sure. A mate did root it but ive put it back to factory firmware 4.1.2 as I didnt like the Revolt he put on it. when I bought the phone I think it was gingerbread.
And im using the factory email app. Ive always used it.

 

The normal factory email app. Just set up to outlook, doesn't push through anymore

 

Did that, I downloaded outlook app. Bought somethin from amazon and straight away I got a notification.
So does that mean there is a problem with the jellybean firmware?

 

Sorted it
Upon reading through outlook app's support pages I had to manually set up my email account and change a few things. Tested it by sending myself an email and it came through.

So that's done, just got my rotation to sort now.

 

Yup don't remember setting it up last time