I have this same problem, and I think I figured it out. The issue is that the earphone is intermittently not charging in the case. Here is how I figured t out. I read these comments and thought I should try and update my firmware. I went to the beats page to do that, but it wouldn't move past the page where it asks you to connect the case with both earphones inside. However I did have both earphones inside the case. This was the first clue.
I then started to suspect power, so I unplugged the case and opened my iPhone to the first page where the battery levels are displayed. I normally would see three battery levels: one for the case, one for the left earphone and one for the right earphone. However, I only saw two - the case and the right earphone.
My theory was that the reason I couldn't get the left to connect wasn't a connection issue per se, but instead it was the fact that the left earphone had 0% battery, and was dead. I tested this by carefully placing the left in the case and left it for 30 mn or so, and then checked the phone battery levels again. This time the left showed with 3% charge. I lifted it out of the case and placed it in my ear and it connected. It then gave a weird tone and shut down again, likely because the battery level was so low. I then left it for 8+ hours and when I came back, it showed on the iPhone at 100% battery and connected fine after that.
I have two use cases:
1) it won't connect initially, but when I put it back into the case and remove it again, it then connects fine. My theory for this use case is that it still has a charge, but when placed in the case the last time I used it, it didnt connect to the case and therefore "timed out" somehow or lost sync with the right earphone. This can be tested by taking both out and listening to them, then only place one back in and leave it that way for a while. When you come back I will bet that the one you left out of the case will not initially connect, but will connect when placed back into the case and removed again as that causes the earphone to sync up with the other one again.
2) It wont connect at all. In this use case, my theory is that the earphone did not connect to the case properly when it was last placed in there, and enough time has passed from the last time I used it that the battery has drained completely so it wont connect at all. Leaving it then in the case for "30 minutes" or so might give it enough charge to work again after that, as some posters in this thread have experienced.
I am having these replaced and hopefully that will clear it. I am not sure if it is a problem with the left earphone itself not connecting to the case for power, or if it is the case itself that has the connectivity issue. Hopefully replacing both will solve it. I certainly will be paying close attention to the battery meter in the iPhone to determine if I am getting a good earphone/case connection going forward...