I have a Netgear N600 WNDR3400v3 updated
to the latest firmware in my house..

I recently moved into a new apartment and about a week ago we started noticing
a very annoying problem...

The router will lose internet connection at random times, SOMETIMES the internet light will
go orange other times it will be off completely. I've tried calling my ISP and they haven't been
particularly helpful.. I was wondering if there was maybe some sort of setting that could be
causing this to happen?

You recently moved. - Right?
The N600 WNDR3400v3 does not have a modem.

I would guess the issue is with the modem.

What modem do you have?
Is it from the telephone company?
From the Cable TV company?

The ISP MAY need to revise or verify the connection to modem . Some modems are very sensitive to changes to changes in wire or able loss.
Id have the ISP send a tech out to your HOME to test the cable. Far greater PROBABILITY that there is an issue with the ISP GETTING their service to you vs your own hardware being the cause for this specific type of issue.