Same problem here. At first I thought sensor of Hall broke. But then I really REALLY hard (but gently :D) clean the contact pins inside charging case and also on earbuds. It helps for 1 more charging. After that nothing helps. Sometimes they are starting to charging by themselves. I'd like to return charging case. But I live far away from the country I bought them. I don't know what support will suggest me at the end but right now suggested option is unapropriate. Nice earbuds, shit case. Also only few unpleasent options to get a new one . Even though you can buy it costs 40$ on official site for 3 part of plastic, 3 schemes and a dozen of LEDs. It's hillarious. If I'd know this kind of problem happen and there is no adequate options, I'd rather check opportunity to buy replacement parts.
I'm having a similar issue with my pair. I can't charge the case anymore. When i push the button on the back like you do, nothing happens on mine. WHen i put it to charge, the first light blinks and will stay like that for hours on end and it will get charged. Did you ever manage to find a solution?
I found a video where a guy fixes same issue for galaxy earbuds via WD-40 ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-7Xynrkw61uM.html . I have another lubricant. I did apply it. But I had to make a lot of forced presses on pins. And I found the concrette one that is failing. WARNING! Lubricant can damage plastic. Unfortunately lubricant didn't solve the issue completly, but it helped. Then I bought 90% ethanol, I repeated presses and it helped. I don't know how long it will be continue. But the problem is in Pogo Pins in my case and perhaps in this case too. Update. Earbuds charged fully one last time and right now case don't charge them. Lubricant and ethanol don't have any influence anymore.