It took a long while but someone found this for me
http://answers.microsoft.com/en-us/windowslive/forum/livemail-email/synchronization-error-0x800488eb/444b79cb-7512-47b7-8787-43c64e6e8fde
The insert below is the very last post on pg 26 from a long survey done on the answers.microsoft.com forum with respect to this issue...
¡Firedog replied on October 31, 2014
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Friday 31 October 2014, 12:38 GMT
@Everyone
The error you're currently seeing, 0x800488EB, is a server error. It shows that there is a fault with establishing the secure channel through which traffic between the client Windows Live Mail and the server mail.services.live.com should pass.
It most probably means that the SSL certificate used to identify the server is invalid for one reason or another. There is nothing you can do about it: the system administrators will have to renew or otherwise mend the certificate. Until they do, you should
use webmail to access your account.
One workaround is to change the date on your computer clock, back to a date before the certificate was invalidated. 15 October should do. You should then be able to synchronize the account again, then change the date back to the current date. The workaround
should remain in force until you sign out or close Windows Live Mail. After that, you'll have to screw the clock back again.
Some people at Microsoft are aware of the problem and may be working on a solution. This will happen at the earliest when Redmond wakes up on Friday, in a couple of hours' time from now.
Please ignore any hoops you may see it suggested that you jump through like reconfiguring, removing and re-adding the account, repairing the Windows (Live) Essentials installation, uninstalling and re-installing Windows Live Mail, re-installing Internet Explorer
and all sorts of other fanciful remedies that won't help. Luckily, most of them won't hurt much.
Well done Microsoft, you don't have the decency to post any info about this causing users of your software to waste hours trying to fix it losing lots of settings etc. And you wonder why people are going off your software.