I emailed a description of the problem to Klipsch customer support. I just received the following response:
I am very sorry to hear about the issues you are having with your second set of Image ONE Bluetooth headphones. This sounds like an issue with the battery. What I want to do is send you another pair to get you back up and running. Once you receive them, please let me know and I will send you a shipping label for the defective set of headphones, this way we can get them in for evaluation. I have placed an order for a new pair of headphones. You should be expecting the item within 5-7 business days. I will include an order number below. Again, I am truly sorry for the inconvenience.
You might want to contact them directly yourself. At least this time they're willing to ship me a new set before I have to send back the defective set.