What are the general problems faced for maintenance in fuel inerting systems?
As far as commercial airliners go, the inerting system is relatively simple and lightweight; see the below diagram from Airbus for a relatively representative architecture (most systems also have some kind of compressor to inert the tanks more quickly in certain situations). 


With a total weight of just a few hundred pounds and the ability for most of the architecture to be colocated near the fuel tanks, the inerting system is far less complex and heavy than, say, the air-conditioning system. The air separation module (ASM) is practically the only unique component; most other maintenance issues with inerting systems are similar to those of other systems: mechanical/thermal fatigue and failure, software bugs, accidental damage, etc.

However, there have been some issues with the reliability of the ASMs, which is currently the biggest concern of aircraft operators. I can't find any public information on why so many ASMs are failing at half their predicted service life, but I imagine it has something to do with their being a relatively new mechanical technology on commercial aircraft.