The fix

Another pair of earbuds broke. This time they were just a fairly cheap pair and one of the earbud covers got a bit disconnected and then ripped off at the wire when in my pocket. Whoops. Two whole weeks. Then I realized that the problem with my Apple earbuds was that the left earbud was off and on not working. I am guessing I am having this problem because the iPhone 6 is big enough that while in my pocket the earphone plug exits the pocket at a level where more pressure is applied to a sensitive part. It wasn't only Apple's earbuds that suffered this damage. I think I have lost a few pairs already to this.

But the right earbud worked fine. Dangling the other one was annoying and having it plugged in was no good either since it went on and off sporadically. So I set the iPhone to output from the right sound channel only... and the headphones work fine now. The left earbud is actually a bit lower than the right, but they work. For now, at least.