You can now fix the pairing issue between your nexus 7 and Nyko playpad without a factory reset or even a device restart. This may also work for other bluetooth devices with similar problems. (Like the playpad pro)
Make sure your device is rooted before trying this or it simply won't work. Also make a note that I'm running stock android 4.2.1 jelly bean. For other devices and/or android versions look below.
Also I am not responsible for any damage done to your device. Especially, that which could be caused by deleting the wrong directory.
First open a terminal and then type these commands.
su rm -rf /data/misc/bluedroid pkill com.android.bluetooth
Now your playpad will pair correctly with the nexus 7. I suggest you make a script out of these commands for ease of use. I am sure you will need to use them again.
FOR OTHER DEVICES/ANDROID VERSIONS:
These commands should be able to easily be adapted to other devices. Just find the directory that has your bluetooth configuration data and delete it. On jelly bean it is apparently /data/misc/bluedroid but for other android versions it could be slightly different. Use a root file browser to find it. But I think most people will be able to find their bluetooth configuration somewhere in /data/misc.
Also the name of your bluetooth process may not be the same. To find it type "ps" in a terminal. It will spit out a whole lot of text. Look at the names on the right and try to find "com.android.bluetooth." If its not there find something similar and substitute it in the pkill command.
Enjoy your gamepad.