C3000-100NAS vs. Macbook

I have an odd case that I can't find the answer/solution for. It seems as though my Macbook is disconnecting the wifi from my modem...

Every time I'm on my Macbook Pro Retina (early '15), the wifi on my modem is affected: the wifi occasionally shuts down. The wifi LED light is on on the modem, but there is no wifi connection. Sometimes it takes a while for it to happen, but whenever I'm downloading something, it disconnects sooner. For instance, I'm unable to continuously download any games larger than 100mb nor my iTunes playlists because it disconnects/affects the wifi. It only happens when I'm on my Macbook... I have no problems with the wifi whatsoever whenever I'm using my PC (with a wired connection), iPhone nor iPad (both wireless obviously), sometimes going days on end without the wifi getting affected.

To fix it, I used to power cycle the modem, but I recently found out that turning off the wifi and turning it back on works for a short while; I'd have to physically walk over to my router, press the wifi button for about 10 seconds, wait for the same amount of time, then press it again to turn it on again. I've tried everything from changing my broadcast name, channel, mode, security options, turning off guest, lowering the fragmentation length, and so on.

Whenever the wifi gets affected, my PC (with a wired connection) can still connect to the internet. My iPhone will disconnect from the wifi and when I try to reconnect it under settings, it'll show the broadcast name but will prompt me to put in the security password which will get rejected. My Macbook shows it's still connected to the wifi, but no internet whatsoever.

My ISP is TWC and my modem's firmware version is 2.02.08. Here's a snippet of the current log:

Is it the modem/router, or is it my Macbook? Any help or suggestions would be greatly appreciated.

(During the writing of this post, I am trying to download an iTunes playlist at the same time. The wifi got affected twice.)