AFAIK, there is no way to have it log in for different users. You could have it log in everyone as 1 user, or just as a guest, but that would defeat your security model.
I think it may just be a limitation of iOS or FM Go that it can't hold the session through switching apps. I could be wrong there.
As a possible work-around, you could build in another layout that could act as a calculator, or build in the specific calculations that your users are looking for. I don't know your application, so I don't know if that is a feasible solution or not.
One other possibility… though I haven't done this myself so I don't know if it is possible or not…
would be to have the file set to auto-login, then have an opening script that could check the system OS (and username?) to automatically re-login the user as the correct account. I'm sure someone else here could tell us if that is even a possibility.
Of course, this also would be a security issue, as it would be somewhat easy to spoof a user and have this script log them in as a legitimate user.
Edit the Extended Privileges (File>Manage>Security…>) and add fmreauthenticate10 if it's not already there. (Replace the "10" suffix by the number of minutes that you want to allow before the users must re-enter their passwords.)
Uncheck "Require re-authorization after the specified minutes…" in the user accounts Privilege Sets to disable re-authorization altogether.
Make sure you use the extended privilage set 'fmreauthenticateXX' where XX is the amount of time for which it holds their login details, for example i have about 20 consultants doing their time sheets and logs on the iphone and have the privilage 'fmreauthenticate10' which means it only needs to reauthenticate a login after 10 minutes
ALSO i strongly believe in handing the security to the actual iPhone and making sure it auto locks all the time and then allow automatic login to the iphone app
Hope this helps, other option would be to have an auto login then control security from inside the APP