DDoS?

Hello! I have a bit of a weird situation. I'm a game developer by hobby and I created an online game that became semi-popular.

I run two game servers from my apartment, and get about 800 different connection attempts to my network hourly.

Players can usually connect to my game servers just fine most of the time, but sometimes my modem (im guessing) appears to enter some sort of "stealth" mode and will reject all connection attempts on the port the game is using. This will go on for a few minutes to an hour, or if I stop the game servers for a little to bit "cool off". When this is happening, my internet itself runs fine so it dont think its a bandwidth issue.

My first guess was my game code of course but after a lot of testing and noticing some of my players who host their own servers don't really have this issue, I'm wondering if my modem has some sort of DDoS protection enabled on it or something, or perhaps the Cox cable connect itself?

Would this be true? I guess what I'm asking is if there were a ton of connections attempted to my network, would my modem or ISP connection enter some sort of protection mode, mistaking this as a DDoS attack? The modem model is CG4500BD.

If I'm right, is there any way to turn it off? Either on the modem or through Cox itself. Or maybe is there a modem that I can purchase that WOULD let me turn it off?