This is weird. It started happening yesterday, I have push email off but I keep getting new mail in the Inbox. Is it possible that if you have mail app in the multitasking bar it will keep checking for new mail?
That's poor on apples part. Being a pop3 account it has to be fetching in the background.
Happened to me too: i think this is related to the poor battery performance in ios4. Try to read this: https://forums.macrumors.com/posts/10480575/
Did you notice when happened? For me sometimes receiving a text message, browsing contacts or browsing recent calls, and immediately mail app start receiving new e-mails in background despite no push, manual fetch etc...
No particular instance. I just started getting new mails without checking when the phone was in standby. I wasn't even using the phone.
Is your battery ok? Just out of curiosity, i've solved my problems about battery drain in ios4 because of this issue.
Yahoo Pop3 pushes to the iPhone.
My battery seems fine. I have iphone 4. it's better than my 3GS.
What about google? I was using gmail (setup as gmail account and not as exchange account in mail)