There is a current epidemic of people failing to access their Hotmail e-mail accounts because Microsoft is experiencing problems with their Exchange Active Sync (EAS) service. The problems are intermittent, so access to Hotmail e-mail accounts are also intermittent. This is the case for me. Microsoft says they are working on the problems. Read about it
HERE.
On the other hand, perhaps your setup for accessing your Hotmail account is with error. This is how I successfully setup the Sony tablet's stock e-mail app to access my Hotmail account.
1. Open the tablet's stock e-mail app, touch the settings icon, and select Settings.
2. On the Settings screen, touch Add Account.
3. On the Account Setup screen:
3.1. Next to E-mail Address, enter full Hotmail account e-mail address.
3.2. Next to Password, enter Hotmail account password.
3.3. Touch "Send e-mail from this account by default." to select/check or (my choice) deselect/uncheck.
3.4. Touch Manual Setup button.
4. On next screen (Account Type), touch Exchange button.
5. On next screen (Server Settings):
5.1. Next to Domain\Username, delete existing text and enter full Hotmail account e-mail address.
5.2. Next to Password, enter Hotmail account password. Note: It should already be entered correctly.
5.3. Next to Server, delete existing text and enter m.hotmail.com.
5.4. Touch "Use secure connection (SSL)" to select/check it.
5.5. Touch "Accept all SSL certificates" to deselect/uncheck it.
5.6 Touch Next button. Note: Here is where you may experience a problem connecting to the e-mail server. If you receive a message saying it cannot connect to the server, wait a few seconds and touch the Next button again. You may have to repeat this step several times before you will successfully connect to the server.
6. On next screen (Account Options), select/check or deselect/uncheck the settings as you see fit and then touch the Next button.
7. On the next screen (Your Account is Set Up and E-mail is On Its Way!), rename the account if you want to, then touch the Next button.
8. When returned to the e-mail app's main screen, select your Hotmail account and you should see your e-mail messages. You may have to touch on the Refresh icon to have your e-mail messages retrieved.
Good luck.