Suddenly logging out of pages
1. There's no BASE_URL, you're editing the site likehttp://site.com but when viewing the URL ishttp://www.site.com. Different URL different session.
2. Cache, try to disable (not just clear) the override cache and possibly all other caches too. Just for testing.
Sounds like something is interfering with session stickiness, if you can't get to the bottom of it - check the headers that re being returned, ask your host if they've changed anything while you check everything else. You could also switch to db based sessions to test if the issue is filesystem based.
Sorry only just seen this reply. If I log in using my customers login it's fine, it just seems to be her machine. If i had the issue you are talking about, would I notice it when editing the site on all devices, or just one?
How do I check the headers that are being returned?