We've had a similar experience. My wife uses an original iPad (IOS 5.1.1) for her email and Web browsing. I have an iPad 2, and we both use our home wifi network. She uses Hotmail—more precisely, *****@live.com. Yesterday, she started getting the "Cannot connect to the server" error when she tried to send mail. Most (but not all) incoming mail arrived as expected. I reset my modem and router, but that didn't change anything.
I sent a test message to her from my iPad—it didn't arrive. I researched this problem at Apple support, where I read that I could try deleting her mail account, then add it back in. I deleted the account, then added it again by choosing the "Hotmail" button from the list in the iPad settings. I opened the Mail app and let it build the inbox. My earlier test message appeared, along with a couple of recent messages.
Then I sent a test message from the Mail app to my own e-dress. The message arrived in my inbox in Mail on my iPad2. I replied; the message sent from my iPad, but never arrived on my wife's iPad. Instead, I saw an error message: "Cannot get mail."
So I again deleted my wife's Hotmail account from her iPad. Next I added the account again, but this time I used the "Other" choice from the list in Settings. When I opened the Mail app, the inbox re-built again ... but this time I got a long list of messages going back several days or weeks. Among them was my reply to the test message. That looked good, so I sent myself another test message. From my own iPad2, I replied to the test message. The reply sent, but again it never appeared in the inbox on my wife's iPad.
Next I opened Safari on my wife's iPad and logged into her account in Outlook.com. (Formerly Hotmail.com, then Live.com ... not to be confused with Microsoft Office Outlook ... it's confusing, I know.) At Outlook.com, I found a complete inbox, sent items ... everything. I've logged into her account on my MacBook, too, so I know her account is working properly. The evidence so far points to a problem in the Mail app on my wife's iPad. I hope someone here can point me to a solution.
