scrabble, there is a certain level of reasonable expectation that a device, looked after appropriately and not dropped or trashed in any way (normal wear and tear discounted) should last for a number of years
Yes, there are built in redundancies that can cause devices to operate at a slower rate, as new software updates are designed for more recent models. However, in your case, you don't have a 3 year, refurbished iPad, you have a two year old refurbished iPad.
So, there is a certain level of "Good Faith" expectation that Apple is very aware of worldwide. I live in Australia and our consumer laws, nationally, reinforce this relationship between consumers and producers. I'm sure that there must be similar guidelines, at least, in your state that will cover "reasonable expectations" when a person makes a purchase of this kind. Particularly as this device is exhibiting a similar problem to the original iPad that you had.
One other question that I have is are you connecting your IOS device to Mac, or WIN?
There is actually one other option worth pursuing. It isa drastic one; but often worthwhile. It is always possible to take your iPad back to factory settings and rebuild the system on your iPad from scratch, rather than simply from its previous profile. By doing it that way you could install only those Apps that appear to be causing the problem (apart from the default apps that come with the IOS) and running them in a clean environment to see if, in fact it actually is the apps causing the problem. Going back to ABC is often a healthy practice.
I know that there is a lot there. But, it is "A" way of rethinking the problem, to find "A" solution.
I hope that this has helped.
Graham