iPad Air 2 shutting down

As described, your iPad Air2 may have a fault. If still operating on its original battery, this will be approaching the end of its useable life.

The Air2 cannot be updated to iPadOS 16.x or later - iPadOS 17.3.1 being current. While the Air2 has continued to receive occasional point security updates (the most recent being iPadOS 15.8.1), the period that updates will continue is unknown. Perhaps consider that update support is typically five to seven years; the Air2 is the only model to have significantly surpassed this - being well into its twilight for support.

For many, expending any effort in fixing an iPad of this age would be folly. Replacement with a much newer model would be recommended. Of current models, even the entry-level iPad9 has specifications and capabilities that will massively outperform you current iPad - runs iPadOS 17.x - and is compatible with the vast majority of current Apps. Other models are more powerful still.

One other thing...

While the iPad9 may well be adequate for your needs, this entry-level model is itself already two years into support.

Whichever iPad model you choose, you would be well advised to carefully consider your internal storage needs - as internal storage (and other hardware) cannot be changed, upgraded or extended. The available internal storage is fixed for the entire life of the device. If you run out of internal storage for your documents, photos and other data, you will forever struggle and become a source of frustration. It is far better to have more storage than you need, than to need more storage than you have.

A good rule of thumb is to quantify how much data storage you will need - add a healthy margin - then double it. If you are unable to quantify your data storage needs, it becomes more difficult. Whilst I and others cannot make definitive recommendations for your personal needs, objectively I would council against purchase of any iPad with any less than 256GB storage, 512GB and higher perhaps having a greater margin for growth.

Within the Apple Support Communities we see regular tales of woe and disappointment when storage requirements are exceeded, necessitating replacement of the device; by contrast, we never see complaint of having too much available storage. It is relatively easy to fill limited internal storage space; perhaps consider higher tiers of storage as providing room for growth as your needs develop or mature - potentially extending the useful usable life of the device. 

Also consider the functional differences between WiFi Only and WiFi+Cellular models of iPad. Aside from the obvious Cellular functionality, only WiFi+Cellular models include GNSS/GPS location capabilities - which may impact any Apps or features that require accurate and consistent location data, such as Mapping. 

Purchase of a WiFi+Cellular model provides access to precise location services, but does not commit you to using Cellular connections. WiFi Only models of iPad have no Cellular or GNSS/GPS functions at all.

Be aware that the iPad9 is the current entry-level model. Other models, such as the iPad10, iPad Air5 and iPads Pro are significantly more powerful.

You can compare available models (and older models - such as your Air2) here:

iPad - Compare Models - Apple