(See the best response by Lummox JR.)
This error is concentrated in side scrolling fighters. Whenever I attack someone by inputting C+down-arrow-key, further C inputs aren't recognized in the game.
Best response
This isn't a BYOND issue; it's your keyboard.

Generic keyboards have limited wiring and are only able to take so many keys at once; certain combinations might allow more keys. What you need to solve this issue is a gaming keyboard. Those are designed for more simultaneous key presses.
I suspected as much, thank you for the confirmation