Hey
Sorry to hear you are having issues.
The first thing I'll ask is if you are on the old Email system or if you have a Microsoft Live hosted email. Then we can look a bit closer.
Pop3 or MAPI? On the desktop, What app are you using? We can look into the settings and see if there is something odd in settings. If, for instance you have put in a "Do Not Disturb" setting, although this is unlikely to affect that sort of thing.
So If you send yourself an email, does it come in right away, or is there a delay?
I'd also check to make sure your email on the server isn't full. I don't beleive there is a limit on the Windows Live hosted emails, but there IS on the Bigpond Webmail, and I'd like to see if that is a cause, because if it's full, it will stop, until you delete and free up some space. So in the settings on your client (whatever client you are using) on the PC for instance, you might have a setting of "do not delete mail on the server" or some delay before you dlete mail from the server.
Yes, - this would affect delivery to the iPad and iPhone, because it might be the PC that is holding things up, and if there was no room for more emails, you would expect to see this sort of thing.
It kind of has those symptoms, so Login to Webmail if you have it stored on Bigpond and just check (I no longer have Bigpond hosted email, so I cannot do a screen cap of what to look for - it takes me straight to Outlook on Windows Live).
and finally, I've seen an issue where a corrupt email coming or in your outbox has caused issues, but I don't think it's that, it really does sound more like a full mailbox if it's been happening over the past weeks.
Come back and let us know, and we'll work through it.