Well, me too suffering from it. I own an iPhone6 and I can clearly see the responsiveness going awfully bad. I was reading about it and found that similar thing was done earlier as well older versions of iPhones that ended up being almost useless after the upgrade.
I used to stay away from the updates but then there are some banking apps now that fail to work in case you wont upgrade :( ... Had to pay the price and now it feel like what deals are on new phones to get one :D :D
They have launched a battery replacement program and you can get your battery replaced for 2,000 rupees which used to cost 7000 earlier. Then your device will return to its full performance. It is not about updates I think. It is just about a degrading battery.
Hmm, I will try to visit their store over weekend here and check it out. But, thanks for sharing this update as I was not aware they were ready replace the batteries at discounted rates.