Why will the latest security update not download on my IPAD?

If you're talking about iOS 12.5.4 (the most recent version supported by an iPad Air 1st generation), what happens when you try?

Are you updating your device wirelessly or via computer?

Should be the former, see this support article:--> If your iPhone, iPad or iPod touch won’t update

If the issue persists, try to update it via computer running iTunes (PC) or iTunes/Finder (Mac).

If the issue still persists, describe the error messages you are getting.

Regards

Giulio

Whether or not you are able to update your iPad to a newer version of iOS/iPadOS will be dictated by your iPad model - and the currently installed version of iOS. You can find this information here:

Settings > General > About

Not sure which iPad you have? Identify your iPad model.

Here is a list of the highest version of iOS supported by the older models of iPad (for simplicity - “generations” are shortened to a number) that are restricted in their ability to be updated:

iPad1 - iOS 5.1.1

iPad2, iPad3 and iPad mini1 - iOS 9.3.5 (WiFi Only models), iOS 9.3.6 (WiFi & Cellular)

iPad4 - iOS 10.3.3 (WiFi Only), iOS 10.3.4 (WiFi & Cellular)

iPad Air1, iPad mini2 and iPad mini3 - iOS 12.5.4

Newer models, not appearing in this list, are all able to be updated to the current version, iPadOS 14.6

The tags appended to your post suggest that you have a first generation iPad Air (a.k.a. Air1). A first generation iPad Air can only be updated to iOS 12.5.4.

Apple ended major update support for the Air1 in September 2019 - although it since continues to receive “point” security updates. The Air1 cannot be updated to iPadOS 13 (or any later major versions of iPadOS) as the internal hardware does not meet the minimum technical requirements (CPU and RAM) for newer versions of iOS/iPadOS.

Some App developers have dropped support for iOS versions preceding iOS 13.x for technical reasons (often because APIs or software libraries upon which they rely have been updated in the new version of iPadOS, making their App incompatible with earlier versions). 

Whilst many App titles remain compatible with your iPad, if you want or need to access to Apps requiring the most recent versions of iOS, you’ll need to consider replacement of your iPad with a newer or current model that supports iPadOS14.

Sorry, I appreciate that this may not be what you were hoping to learn.

I hope this information provides helpful clarity as to your available options - and the fundamental limitations of your existing iPad Air.

.