ipad2 model MC755LL/A won't retrieve update 9.3.6

We were discussing things that should be able to update over-the-air, claim there is an update available, but for some reason do not load the update and just sit there spinning. In the end it will not load it over wi-fi, one must resort to using iTunes.

In most cases if a device saying it is up-to-date then nothing will get it to load a newer iOS. 9.3.6 is a special situation in that it is an update for a very small set of hardware that Apple long ago stopped supporting.

You may wish to read:

"Update your iPhone, iPad, or iPod touch" --> https://support.apple.com/HT204204

and:

Update your iPhone or iPad software to avoid issues with location, date, and time - https://support.apple.com/en-us/HT210239

I had that problem with an iPhone 4S (I tried 3 times) and I had to not only connect it to iTunes, it has to be to iTunes 12.8 or newer on a computer capable of supporting iTunes 12.8. So no attaching it to my wife's 2013 MacBook Pro with iTunes 12.2 even though that definitely supported iPhone updates in the past. Presumably a computer with Catalina could do it too. If not, take it to an Apple Store.

Whoa, back up for a moment.... older devices that cannot update through “Software Update” in settings can be updated with iTunes? What limitations are there?

I have:

iPhone 4 running iOS 7.1.2

Software Update reports “Your software is up to date”

iPad Mini 1st Gen running iOS 9.3.5

Software Update reports “Your software is up to date”

iPad Air running iOS 12.4.3

Software Update reports “Your software is up to date”

Can any of these devices be updated, and if so, how far? Surely I could not run iOS 13 on my iPhone 4.... right?

Try to update with iTunes instead on a computer, it does look like you have the iPad 2 Cellular CDMA model which needs the update to 9.3.6.

You are welcome.

You are welcome, though I don't know why I wasted my time since apparently my initial post was ignored after I made it, though it told you what you needed to know about updating using iTunes.