When they change their password, have it emailed to you? Or emailed to themselves?
When they change their password, have them write it down in three places and tape one to the ceiling?
There are commercial filemaker recovery software, have never used one. Explain that they will have to buy the utility if they lose it?
About Passwords http://fmforums.com/forum/topic/56971-create-a-password-field/
A little human engineering may be in order such as making it a policy to bill them for the time you spend restoring the password. That compensates you for your time and encourages them to not lose track of the password. A simple piece of paper kept in a safe or locked file cabinet (safe is better if info is truly sensitive)--and this something you can recommend to them should be all they need to keep this from happening.
And you might want to strip out the admin account from the run time and use a non-admin account combined with a script (set to run with full access permissions) to reset their password for them so that your run time copies are better protected.