I had the alternator go out in my '07 G35s but not until it had hit 8 years old and 125k miles. The alternator in my '08 G37s never failed (had it 9 years and 85k miles) nor my current '14 Q50s (7 years old @ 80k miles). What does that mean? Well, nothing really. Alternators are simply not a component that is known to fail often in these vehicles, but obviously they can. Try to get a new alternator vs. re-manufactured if you can. VStar makes a great point as to validating it's actually the alternator with the issue, when mine failed it was easy to determine as I was on the highway when the car went into "bingo" mode due to lack of charging and the eventual test of the alternator showed it croaked.
Your car is 10 years old, you will eventually start to have things need replacement that are above "normal". It's why I usually don't keep cars for more than 7 years, in the case of the G37s coupe, it takes Infiniti way too long to release new designs so I had to wait a bit longer.