Is there a backup to fuel inerting systems?
Short Answer

No, it does not have a back-up, there are some fail-safe components in the system(see below), but in general the system itself is not duplicated. The system, together with a design that avoid ignition sources within the tanks, is just a part that contributes to prevent fuel tanks to ignite. An Inerting System for commercial planes have been considered since 1996 TWA accident and first regulation arrived in may 2006.

Longe Answer

The certification CS25.981 Fuel tank ignition prevention states:


  (a) No ignition source may be present at each point
  in the fuel tank or fuel tank system where
  catastrophic failure could occur due to ignition of
  fuel or vapors. 
  
  (c) Design precautions must be taken to achieve
  conditions within the fuel tanks which reduce the
  likelihood of flammable vapors.


So the function that should be achieved is prevent tank ignition and there are two fronts two work on, avoid ignition source, and reduce fuel vapors (similar to the two slices of cheese that rbp was mentioning in the comments). 

So the fuel ignition system is a system designed to avoid fuel vapors. As can be seen in the image below, within the systems there are some redundancies (e.g.: Dual Flow Shut Off Valve), but the system itself is not duplicated. 

Moreover the system is not on the Minimum Equipment List (MEL), so the aircraft can still be dispatched with the system inoperative for 10 days.