Increasing power required with altitude.. what's a good plain english explanation?

No, same IAS, same drag, same thrust, same power requirement from the
engine to generate the thrust. The statement that power is drag time
velocity is incorrect. That is the point where the error is made.

All of the definitions of power that I have seen have been along the lines
of P = T * V, or something that equates to that.

For instance:-

"The formula for Thrust Horsepower (THP) is:
THP = D x V"

from http://selair.selkirk.bc.ca/aerodyna...nce/Page4.html.

That is wrong?