This is why we rule that one source of damage is per creature, not per damage type. Concentration is also fairer for the players at lower levels this way (less checks less chance of failing).
The rules themselves are ambiguous as to what a source of damage is, in any case it's not meant to be per hit or they would have stated that.
By the current rules it is per hit now. A creature claw/claw/bites you making 3 attacks and all 3 hit that is 3 seperate concentration saves. Same goes if four different goblins all shoot 4 different arrows at you, even if they all go on the same initiative.
Now if you mean something like X spell does (2d6)fire and (2d6)radiant damage, that is just one spell so it is only 1 concentration save, only spells that have multiple attack rolls would force multiple concentration rolls if they all hit.