I was told that I'm supposed to keep washing the brown rice with water, empty the pot out, and repeat until the water doesn't become foggy anymore to get rid of the arsenic. For each cycle, I pat, squeeze, and swirl the rice around for roughly 1 minute. I've done this 12 cycles now and the water still remains foggy. Should I keep going or is that enough?
The cloudiness you see in your rinse water is starch, not arsenic.
The amount of arsenic still present after rinsing off the starch and cooking the rice is safe according to the FDA. https://www.huffingtonpost.com/entry/arsenic-in-rice_us_589cc1ffe4b09bd304c0b04c