Keeping multiple login info in facebook?

I'm trying to help my wife out with setting up her new Lenovo P50 64 bit laptop we purchased from Best Buy. By the way, so far I'm very impressed with Lenovo. Anyhow, my wife has a few facebook accounts and to move from one account to another she would just click on the login box and it would show all the accounts so that she would just click on which one she wanted to use. That worked great on her old laptop (windows 7, 32 bit), but on this new window 7 laptop it acts really strange. Sometimes she clicks in the login box and all the accounts are there so all she has to do is click login. Then the next time maybe just one or two of the accounts show. It is really random and doesn't seem to have a pattern. I checked her saved passwords and all three accounts are in there. Any suggestions on how to keep the login information in facebook?

Dirtrider,
Hum, I like the way you think out of the box. I'm not sure if it will work or not but when I get home I'll try it.

Any thoughts on why the account info (login email and password) shows and then doesn't show? I'm sure it's got to be a setting somewhere but I haven't found it yet. To me it sounds like something is clearing the cache on some of the accounts.