My mint did that earlier in the year. I had it in a shady spot and it was quite damp. I moved it to sun/part sun and watered less, about once a week, and it has since rejuvenated. I'm not an expert, though! Someone else might provide some more information.
Thirst and starvation? I harvested my ginger mint a couple of weeks ago to make mint jelly and the lower leaves left behind look a lot like yours - old and tired - and I've had to take to watering every day to get fresh young new growth going. It's had a good handful of pelleted chicken manure too so I'm hoping to see an improvement soon.
Vendée - 20kms from Atlantic coast.
"The price good men (and women) pay for indifference to public affairs is to be ruled by evil men (and women)."
It doesn't like being confined. It's natural tendency is to wander, so it always has new soil to grow in and choose places that suit it best. Hard to match that in a pot!
Another option would be to get it out of the pot, cut it in half and replant it in fresh compost...you can of course transplant the other half and have two plants. They respond quickly to a repot.
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I'm not an expert, though! Someone else might provide some more information.