The page saves and claims everything is fine, but when you refresh the live page nothing has changed, then refreshing the editor will show that the template is still the same as it was before you updated it.
Update, it seems that it is only the Contact page that is being effected for some reason. Activating the Layouts plugin constantly forces it back to the default template, even though I've never used layouts for that page and there is no layout associated with it.
Ok, now I'm not sure. I think it is happening to any page when you update it as I've just observed the same behaviour on the home page as well. Simply accessing it doesn't seem to force it to change so I'm assuming it's something to do with the hook for the save / update function.
It seems to be purely isolated to page templates, nothing else, and it also seems to be nothing to do with using layouts, merely having it active.
If you go to the contact page it should say it is using no layouts and the default template.
If you change the template to either 'contact' or 'basic' and save it then this should change the header bar on the front end to a narrower one with a different positioning for the breadcrumbs and a lighter, solid blue background.
The page with say it updates fine but then refreshing the front end will show no changes and if you refresh or press update again on the backend editor then it will show that the template selected is the default template again.
I deactivated every plugin and reactivated them one by one and it was Layouts causing it. I turned them all back on accept Layouts and it didn't happen, I turned everything except Layouts off and it still happened, so I'm pretty sure it's something to do with it.
Does that make anything clearer? I'd make a video if I could to show you but I don't know how I could get one to you.
I appreciate what you're saying but I could already work around it, I'm trying to figure out what it is happening and try to fix it as it is really irritating.
I've never encountered this with any other installation and generally speaking problems like this are due to some form of database corruption, which this is not. So I'd really appreciate some more digging and trying to figure this out as I have proven to you that Layouts is causing this for some reason.