Apple Pencil is taking too long or even failing to connect and cutting out spontaneously

Try the tips found here in this link below.

Connect Apple Pencil with your iPad - Apple Support

If no joy, call your nearest, “local” Apple Store to make an appointment and have your iPad and Pencil looked at.

If less than a year old, if defective, Apple store will give you another replacement Apple Pencil at no cost.

Best of Luck to You!

What year/model/screen size of iPad and which version of the Apple Pencil?

Prior to this issue, when was the last time your Apple Pencil was charged up and uaed eith your iPad