I wouldn't take it as an issue, myself. Not in regards to my character. Which was your original point, I think?
If I looked at it more closely, did some comparisons with how it stacked up to other characters, super-tough ones, that kind of thing, and came to the conclusion 'This breaks the game', I'd probably suggest tossing it.
If it was just 'a REALLY strong combo', I'd probably keep it.
It busting up my own character in a matter of two hits is not part of that consideration, though. ^_^
Option to make it work: Either the initial core damage does not stack (ie, someone has already taken the 20, they cannot take that again until the persistent damage stops) or the Persistent damage doesn't stack (ie only the 20 damage applies to each hit, damage per turn from a single technique cannot stack, though different techniques from different sources MAY stack).Being able to get 20 Core HP per attack PLUS 5 Core HP DMG per turn that stacks per consecutive attack PLUS the damage inflicted by the attacks themselves is wild. It is not street legal and definitely not in the game.