Q: Should I be able to charge ipad while in recovery mode?

Yes, it should charge. It helps greatly when attempting to get the device out of Recovery Mode.

And you are sure it stops charging, or is it that you cannot see that it is? Why don't you recover the device?

Okay, now we are getting somewhere. See this support document about restore errors. Get help with iOS update and restore errors - Apple Support

Seems the error 28 can be a hardware error. You may want to make an appointment at the Genius Bar of the nearest Apple store to have them examine the device. They can explain your options from there.