Apple Pencil 2nd Gen Not Working with iPad Air 5 After 2 Months of No Use

I’ve been using the 2nd generation Apple Pencil with my iPad Air 5, but now it’s stopped working. Over the summer, I didn’t use the pencil and kept it safely stored in its case to avoid any damage. Now that school has started, I took it out to use, but it won’t work. The Apple Pencil name flashes on the screen, but it won’t connect properly. Unfortunately, the warranty has expired, and a new one costs ₺5,500. I’m really frustrated by this sudden failure after taking such good care of it. Apple, please provide a solution for this issue, as the cost of replacing the pencil is way too high!