One way to deal with the extra checks from burning and stuff would be to make it so you just don't make a check if the damage you sustain from that source was less than 10% of your total HP. That way sustaining only 1-3 damage wouldn't be enough to trigger a concentration check at all. You'd only need to worry about actual attacks.
On the tabletop this would be difficult because percentages involve math, but in a video game it'd be real simple.
