I also experienced problems with brand-new fob batteries, especially ones made in China even if the packaging claimed it was a brand-name item. Strongly support trying to get new, high-quality fob batteries (Japanese manufacturing seems more reliable) and double-checking that the voltage is correct.
As you have mentioned, The Smart key is a nice feature and when it comes to batteries for the Fobs, I dont go cheap. I buy name brand premium batteries with the highest date code i can find. Also, I have found that the fob will cause my phone to drain very quickly and even get warm if I put it in the same pocket. My guess is it is also not doing the fob battery any good. That would not explain why a stored fob would die quickly though. I like the idea of taking the battery out of fob that is stored only for emergency.