Hope this fits in the right forum...

I have a freshly made outlook.com email account (not a converted hotmail.com account) set up in the Microsoft Mail app in Windows 8.

Most of the time, emails come and go as they should. But there are some that are not appearing within the app. If I login to outlook.com via a web browser, there are new emails sitting there that have not synced with the Mail app. Some emails from the same sender appear in the mail app, some don't. 

I have tried uninstalling and reinstalling the mail app, makes no difference. I have added the account to the Mail app on a different PC, one with Windows 8.1 preview installed, the same emails still don't sync through.
I have also added the account to the Windows Live Mail desktop app, and the 'missing' emails DO appear there. 

So it seems it is only within the stock Windows 8 Mail app that the sync issue is appearing. As far as I can tell, this has only been happening since last weekend when Microsoft had issues with their outlook.com server or something. There are about 8 emails across last weekend that haven't shown up, plus 3 more since Friday just been.

Googling finds a few other people who have struck the same thing dating back to last month at least, but no solution.

Any suggestions?

The account in question is that of my 80ish year old Grandma, who has only just got the hang of the touchscreen laptop she now has and the mail app, but I'd really rather not have to try to teach her to use a web browser or a different app.