I've seen reports about this, but unfortunately it's not an extremely common thing. The verdict is in fact still out as to whether its a bug with the software/firmware or its some other application/task killer or state that causes this. It can be caused if you have a gmail account open on say your computer which refreshes and finds the new mail first, but that case would probably be recognized and thus isn't the cause for most people.
Try going to settings -> applications -> manage apps -> menu option -> filter -> all. Then find Gmail and Gmail Storage. For both, click the clear data button. NOTE: This is 100% safe, it does NOT kill your accounts and you do NOT have to resign up your google accounts on the phone. It simply kills the data. This maybe help.
Also, make sure you dont have a task killer blowing away important processes.
The 4 day setting is in the gmail app itself in account settings. And that is for how many days to synch with. That is NOT the same thing as having the email pushed to your account immediately. Synching is to a process that runs periodically and synchs up the inboxes (i.e. if your phone was off for 2 days, when powered on, synch will bring over even old/seen emails.