I really wouldn't know what could cause this. Does Remote Buddy turn 
up in "Activity Monitor" (/Applications/Utilities/) after you double 
clicked it? If yes, please select Remote Buddy's entry in the list, 
use the "Analyze" function of Activity Monitor and send the output to 
info@iospirit.com / use the contact form.

If it does not even turn up there, I have no idea of what could be 
going that wrong (except a corrupted binary or wrong permissions).

A fresh install should always work, though. So you might want to 
completly remove Remote Buddy.app, enter

mkdir ~/Desktop/OldRBSettings

and then

mv ~/Library/Preferences/com.iospirit.*emote*uddy*.plist ~/Desktop/ 
OldRBSettings/

in an open Terminal (that'll move all your existing Remote Buddy 
settings to your desktop in the new folder OldRBSettings). Finally, 
download a fresh copy of Remote Buddy, drag Remote Buddy.app to / 
Applications and start it from there. If you end up performing the 
fresh install approach, I'd appreciate if you could send me 
(info@iospirit.com) a copy of the files in OldRBSettings to try to 
reproduce the problem here and fix any bugs that might be responsible 
for this.

Best regards, 
Felix