I just test it with tyr. It appears that it takes the damage left on the current stack and adds it evenly to each turn when it renews. For example my Tyr does 268 or 67 per turn. I had 2 turns left or 134 total when I did a second hit. It reset to 4 turns at 101 per turn which would be the 134 left + 268 new = 402 or 100.5 per turn round up to 101.
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