Did you install Remote Buddy in /Applications or elsewhere?

Do you run as admin user or user with limited rights on your machine?

What happens during an update of Remote Buddy itself is this:

1) Remote Buddy downloads the latest DMG file (the one you get from 
the website).

2) Then launches a special tool inside Remote Buddy, that mounts the 
DMG in the background and replaces the old copy with the new one.

3) Launch the new version of Remote Buddy.

Since it will only offer you to proceed after step 1 if the download 
completed successfully, the problem is probably located in step 2. As 
Remote Buddy uses standard system tools to achieve what it does 
there, the only two remaining error sources I can see are

a) permissions to write to the directory Remote Buddy is located in 
are to restrictive

b) inavailability of the shell commands Remote Buddy uses (corruption 
of those can easily happen while running (any) software while Apple's 
Software Update is running - my source for this is http:// 
unsanity.org/archives/mac_os_x/shock_and_awe.php ).

There may be more possible error sources, but these spring to mind at 
first.

Best regards, 
Felix