"Keep me logged in" not working

We are having persistent claims from the client that this is not working, but I think it is a problem with the client's browser.
Is there a log of sessions that we can see that shows whether users were kept active between sessions? ie they log in at 2PM then close the browser, then re-open at 6PM and continue as if they were still logged in.
If I can run a report that shows the majority of users are not having the problem, then hopefully the client will stop complaining.

thanks
Marcus