Error 0x800488EB

I have two accounts set up in Windows Live Mail.  Both sync just fine from home, one syncs just fine from work.  The other one gives the error:

Unable to send or receive messages for the xxx account.

Server Error: 0x800488EB
Server: 'https://mail.services.live.com/DeltaSync_v2.0.0/Sync.aspx'
Windows Live Mail Error ID: 0x800488EB

Now, this is where it gets interesting.  If I get off the work network and onto an open network and do a sync (which works), then get back on the work network, that account syncs properly from the work network for just about exactly 24 hours, then stops again.

I have done the remove/re-add thing, and there is no change.  Note that this started up on its own one day after having worked fine for many years.

One thing I've noticed that's probably related is that, in Properties-Server-Server URL, the account that works looks for:

http://mail.services.live.com/DeltaSync_v2.0.0/sync.aspx

While the account that doesn't work looks for:

https://mail.services.live.com/DeltaSync_v2.0.0/sync.aspx

Note the secure URL in the one that doesn't work.

It turns out this is happening to others in our organization as well, but like with me not on all accounts.

I'd like to fix this either by finding what to change in the account properties or by white-listing something in our cyber-security system so that it doesn't happen for these accounts.

Thank you.