Apple Pencil 1st gen keeps disconnecting from iPad a16

Your Apple Pencil is exhibiting symptoms of a failing battery - that will not reliably accept or hold any charge. Given its declared age, the battery may simply have reached the end of its useable life.

If the Pencil Battery has failed, the only remedy is to replace the Pencil. You would be best advised to visit the Genius Bar at your local Apple Store or Apple Authorised Service Provider (AASP) - where the technicians will be able to test and assess your iPad and Pencil. If a fault with either is identified, you’ll be in the best possible place to explore your available options:

Genius Bar Reservation and Apple Support Options - Apple

All rechargeable batteries can give false voltage readings, upon which their level of charge is based, as they fail.

Other than the battery, verify that the user-replaceable Pencil tip is snugly screwed into the body of the Apple Pencil; when fitted correctly you should see a tiny gap, of about the thickness of a sheet of paper, between the tip and pencil body. If slightly loosened, or overtightened, the Pencil may not work properly, if at all.

A good diagnostic is to test your Pencil with another compatible iPad; if the behaviour is consistent/repeatable with another host device, you have demonstrated that the Pencil has a fault. If the problem is not apparent when used with another iPad, then you will have isolated the problem to your iPad.

If you don't have easy access to another compatible iPad, consider visiting a local retailer that has demonstration iPads - and test your Pencil there.

Otherwise, visiting the Genius Bar at your Apple Store or AASP provides opportunity to have both your iPad and Pencil hands-on tested by an Apple Technician.