My old iPad (iOS 10.3.4) will not appear on my Mac for AirDrop

Whoa! That's a surprise! I have to be signed into iCloud to carry out the transfer??? Weird!

So I tried it. The iPod claimed to be already accessing iCloud, but I re-entered my password and turned some things off and back on, and gave up. Two minutes later, though, my Mac decided that it did, after all, see the iPad. Huzzah! So I started transferring some images. I got three transferred. Huzzah! Then I spent a few minutes preparing another image, then AirDropped it to the iPad. But in the meantime, the iPad had turned itself off. From there, everything went downhill. I eventually got the Mac to recognize the iPad, but when I tried to transfer the image, the iPad did not offer me the opportunity to accept or reject the transfer, and after a few more minutes, the Mac declared that the transfer had been declined.

After much more random experimentation, I determined that the iPad will NOT accept anything unless it is at the base level (showing the app icons). Moreover, its communication with the Mac is very, very slow. Finally, some luck is required to achieve a successful transfer.

Thanks for the help.

Sorry for the overly concise explanation. Here's a more complete explanation.

I want to transfer a file from my Mac to my old iPad. The Mac is using OS 15.4. The iPad is using iOS 10.3.4. I use Control Center on the iPad to set AirDrop to "Everyone" and AirDrop Receiving to "On". Bluetooth and Wifi on the iPad are turned on and are indicated to be operational. The Mac has Bluetooth and Wifi turned on and they are indicated to be operational.

When I am in the Finder and select "AirDrop" from the panel on the left side of a Finder window, Finder reports "No People Found. There is no one nearby to share with". In the bottom of the window it says "AirDrop lets you share instantly with people nearby. Allow me to be discovered by: Everyone".

So, my question is: why doesn't the iPad appear in the Mac AirDrop window?