From what I've read, configuring Hotmail and Android can be a tad difficult. Do you know if the email account is configured for POP or IMAP?
Check in the settings of the mail app, hit menu, more, settings, send and receive. There should be an option called Download options, what is that set too?
There may also be a setting on your hotmail account online which prohibits the amount of mail sent to the device. With Gmail, there's an option to forward all mail, or forward mail sent from now on.