Hello, can you help me?

I have a laptop with Windows 8.1 fully up to date (to 5 Feb 15). I am using Windows Live Mail 2012 (Version 2012 (Build 16.4.3528.0331)).

I have been using these all for ages with no problem but, suddenly last week, for no reason I can fathom, Windows Live Mail stopped working properly.

I have 4 e-mail accounts on Windows Live Mail:

Hotmail, Gmail, Outlook and Fastmail.

Windows Live Mail continues to work perfectly well in every way with Gmail and Fastmail, but, it now steadfastly refuses to log-in to either Hotmail or Outlook. Instead it gives me this error message twice, one for Hotmail and one for Outlook:

Unable to send or receive messages for the Hotmail (XXXXXXX) account.
Server Error: 0x80048820
Server: 'https://mail.services.live.com/DeltaSync_v2.0.0/Sync.aspx'
Windows Live Mail Error ID: 0x80048820

Unable to send or receive messages for the Outlook (XXXXXXX) account.
Server Error: 0x80048820
Server: 'https://mail.services.live.com/DeltaSync_v2.0.0/Sync.aspx'
Windows Live Mail Error ID: 0x80048820

It used to work fine until last week.

I have tried to re-synchronise the Internet Time with an Internet Time Server but it doesn't make any difference, the problem remains.

I have tried deleting the Hotmail account from Windows Live Mail and then putting it back again manually, but that doesn't make any difference.

I can access my accounts by going to the Hotmail/Outlook website and signing-in. But if I have to do that then what is the point of having the Windows Live Mail client on my computer?

Can you help?

Thank you!