Regarding Bluetooth: 
Bluetooth keyboards only produce very low traffic over Bluetooth 
(basically only when keys are pressed), whereas f.ex. a Wii Remote 
produces a constant stream of traffic and will thus have a different 
effect. If you did not use any Bluetooth remotes with Remote Buddy, 
the Bluetooth part of Remote Buddy isn't doing anything, though.

Regarding Time Capsule crashes, disconnects and the like: 
Physical interferences through the use of a Bluetooth remote could 
have been a possible cause for the interruption of a wireless 
connection. 
With a wired connection, however, wireless signals and Bluetooth don't 
play any role, and I can absolutely exclude the possibility that the 
use of Remote Buddy can in any way cause the problems you are seeing. 
There's no code in Remote Buddy capable of doing any of that.

I remember having read a couple of early reports that mentioned the 
Time Capsule hanging and crashing (=> just google for "Time Capsule 
hang" and "Time Capsule crash" to find loads of user reports). Given 
your description, you may well have gotten one of the units behaving 
that way.

Since this is really a Time Capsule issue, please contact Apple for 
help and a possible replacement.

Best regards, 
Felix Schwarz