Remote Buddy will deactivate all remote controls on a fast user 
switch, so that the user you switch to can use the same (hardware and 
internet port) resources seamlessly. Since the AJAX Remote is a remote 
control in Remote Buddy, it will be deactivated, too, when switching 
to another user.

If all you are looking for is protecting your Mac from usage through 
your children, you can achieve this is another way:

1) Go to System Preferences > Security > General

2) Activate "Ask for password when ending sleep or screen 
saver" (wording may be different)

Best regards, 
Felix Schwarz