Hi,
I'm getting the exact same error, one day it worked the next it didn't so can't be anything to do with my firewall / internet security.  But I did disable it and try to update my mail just to get this out of the equasion and had the same error.

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

I can see my mails on the outlook web version.
I'm using Version 2012 (Build 16.4.3505.0912)
I can't see an outbox in webmail, none there.
I'm running Windows7

Like I said it's been working fine no probs then the next day bummf.....nothing won't work.  Nothing has changed that I know of at my end.

Any help would be appreciated.

Thanks