Welcome to LQ!!!
Here are few things that you should first know about single user mode:
1. You cannot disable single user mode for root user. root user can get into single user mode by typing "init 1"
2. Normal users cannot go do "init 1" unless you have provided the access via sudo.
I believe your users are changing your password by getting in single user mode from grub. If that is the case you can password protect grub by performing following steps:
1. Login as root.
2. Run the following command:
3. It will prompt you to enter the password.
4. Enter the password and it will generate an md5 hash.
5. Copy that hash value (make sure you copy it properly)
6. Edit /boot/grub/grub.conf file using vi or vim as follows;
7. Put that hash value in that file just below the line "timeout" as follows:
[code]password --md5 <copied hash value>
When you will reboot the system you will see that it will not let you edit grub by just pressing "e" you have to first hit "p" to enter the password and then you can edit grub entries.
Make sure that you take a backup of /boot/grub/grub.conf file before making any modifications