Are there any apps that you can't use because you didn't update iOS? Do you also have a Mac and/or an iPhone and if so does it affect your ecosystem? I also have a 3 and I a have noticed some lag only recently. Even though I've had this thing almost 3 years I have just now started playing some games. I've noticed the most lag on those.
I plan on getting an Air 3 late this year or early next year and was contemplating keeping iOS 9 on there as long as I can use all the apps I want and I don't have to update the iOS to keep it working with my other Apple stuff.
For most apps; Apple allows you to download the last compatible version for the version of iOS you own. But there are a few apps which require the latest version of the app to work.
Also, I am not really pushing the limits on the device with the latest games - I use it for mainly media consumption, Netflix, Youtube, maps, email, surfing: all that works great.