We foud our issue with mail on iPad3 was a bad email message was clogging the pipe. It's acualy a common proplem with email not downloading that technacly unrelated to the device or software. One email mesage is ether corupt, has a bad charicter somewhere in the message (usualy in the subject), is too large for the server, and has a corupted attachment. Troubleshooting usualy involves removeing unessary messages from the server. In the case of hotmail going to the hotmail web site and removing the messages from the server so that the mail application no longer attempts to download the offending message. You can also move the messages to a temporary backup and move them back in sections to see at wich section the download fails. We moved all our messages to a backup and moved them back month by month to isolate where the problem email was.
I don't know if your using the mail application to access hotmail, all of that above assumes that your having trouble there. I hope this helps.
iz