I have a similar issue with my 08 G37. Only once has it not turned on. Every other time, it just sounds like it struggles to turn on; but it does.

The TSB has been performed. If i leave the headlights on for anymore than 5 minutes, with the engine off, the car dies.

When i take my car in for service, other newer G37's don't have that same struggle. The service consultant that helps me says this is typical in an 08, however there hasn't been a fix yet

 

I have had the dealer fix my 2009 under warranty for a problem with the battery draining. They replaced some part of the wiring and gave me a new battery under the factory warranty.

Even though you are past the warranty period, it might be worth checking with the Infiniti dealer to see if there is a fix they can do or recommend to cure your problem

 

I got the car back yesterday.
It seems to be starting alot stronger than usual. It doesnt struggle anymore, but its only been 2 days.

I will keep everyone posted.

Here is what the dealer did... (notes on receipt)

Checked DTC codes, no codes stored, checked oil pressure and found normal excessive carbon deposit buildup.
throttle body cleaning - throt
battery passed performance test - no problems found with charging system
throttle body plate - performed throttle body cleaning.
idle volume relearn and ECM/TCM reprogram. test drove vehicle after repairs and found operating as designed at this time.

I will post any updates, thanks again.

 

did you get this figured out yet?

 

@Bsmith062579
You may want to create a new thread with details on your battery issue as this one has not been updated in almost 10 years.