If you have not done so, go to your email's webmail site, and make sure the emails are really being deleted from the server. Be sure to check the Junk Mail folders. The iPad will reflect everything that happens to your email account, whether it was done on the iPad or not; however, it may not update until you open Mail. This means you can often see, briefly, emails on the iPad that have already been moved or deleted on the server.
If it is happening on the server, the problem will probably have to be solved on that end, by working with hotmail's tech support.
If it's only on the iPad, chances are it's settings or a glitch. Open the account's settings in Settings > Mail, Contacts, Calendars to make sure the iPad is set to retain email longer than 3 days, a default that overrides the general settings for all email account. For a glitch the easiest thing to do is to delete and re-add the account. Because all data is stored on the server nothing should be lost.