Notifications are very delayed on android - but only sometimes (apparently FIXED)
One reason could be you have auto-sync turned of which is resulting in emails not being synced automatically.To enable this
Goto Setfings->Accounts &amp; Sync ->tick Auto-Sync 
also select your google account from there and make sure "Sync Gmail" option is ticked. 
Another reason that may cause this can be battery savers. 
Try turning of "battery saving mode" on your device and test again also turn off any 3rd party battery savers if you have any or white list the Gmail app in them.