So I was in an accident caused by another person. I had the body work (front bumper and right head lamp) done at a reputable shop that Infiniti referred me to since they don't do body work. After picking up my FX, the driver side dashboard speaker now turns off and on when I hit bumps in the road. I never had any audio problems before this, not cracking or any speakers not working, nothing. Infiniti told me it would cost $100 to run a diagnostic which I don't want to pay if the body shop had something to do with it. So can anyone tell me if this might be related to a blown fuse or relay that could have been caused by the body shop? Any advice would be much appreciated.

Your Infiniti Dealership should not charge you a diagnostic fee if your Infiniti FX is still within Basic Warranty Coverage.

Most likely this is not a fuse or relay issue, as you have mentioned that the speaker works at times, albeit intermediately. I would speculate that it is actually a loose connection behind the speaker and simply needs to be refastened into it's harness. This would explain why the issue occurs when driving over bumps — as the wire would loosens when your Infiniti FX vibrates to compensate for the stress on the suspension from the bump in the road.