The longer I know kava, I have to say I keep the leftovers in the freezer after two washes, for a last third one.
But the quality of the third one, only exists if you use hot water to help to extract the rest of it. But the effect is always different.
Meanwhile I prefer to do a third wash without freezing it before. But even then, the third isn't the same quality - effect wise. I don't mean the potency, I mean overall.
But it depends on cultivar, some have great qualities when you do a last wash with hot water - like you activate a hidden "bonus" within the kava. But those are rare. Mighty roots f.e. is one of those kavas.
Other third-washes produce headache. If Kava wouldn't be so expensive (especially in Europe), I would throw it away after 2x washes.