No POP or IMAP "Push" Email on iPad?

I have Push turned on. My Fetch settings are currently set for "Manually", but that should be irrelevant if it is pushing correctly which it is not. The iPad is not receiving "pushed" e-mail when I am actively working on the iPad with a full WiFi signal. It will only receive email when I open the mail app itself, at which point it automatically downloads all messages at that time. Maybe that is the full extent of the iPad's "push" capabilities i.e. the Mail app has to be open? Again, my iPhone and iPod both do "push" correctly on WiFi today, they will notify me of new email messages with a tone and number of new messages notification on the Mail app icon, for all of my email accounts, the iPad does not do this. So it does not behave like my iPhone or even my iPod. The only other piece of data that I can think of no pun intended is that this is a 3G + WiFi iPad, but I am not signed up for or using 3G at this point, hopefully that is not the problem.

More info - on my iPhone, two out of four email accounts are Exchange, the other two are POP and IMAP. For Exchange email accounts, there is another option to select "Push" versus "Fetch", but for POP and IMAP, you can only select "Fetch" versus "Manually". Makes perfect sense, until you realize that I am still receiving "pushed" e-mail to those POP and IMAP accounts via iPhone and iPod, but not the iPad. Makes no sense. I just checked everything again, the settings are exactly the same all around. The only conclusion that I can draw is that you simply have to have the Mail app open in order to "pull" new email. Yes, it is really fast, as soon as I open the Mail app, all of that new mail downloads or is already downloaded, very fast, but that is not "push". that is "pull". Is it possible that the combination of the Mail app as it exists on the iPad, plus WiFi, plus the use of non-Exchange email accounts, results in a "pull" versus "push" scenario as I am describing? I mean, it all works, it just doesn't work like I am used to or how I would optimally like it to, but I can learn to live with it. I want to exhaust any and all possibilities before giving up on "push", so any additional insights would be appreciated, thank you.