What you're calling a 'backing plate' is called a platen. They are almost always made out of mild steel. The exception is that, if you plan to use your sander for knifemaking and you plan to use it a lot, you may want to put a different wear surface on it like lilredex suggests above.
However, pretty much every single metalworking and woodworking sander comes with a platen that's made of mild steel (everything from Burr King to Delta) with no extra wear surface. Personally, I own a lot of sanders and belt grinders, and I don't bother with extra wear surfaces -- mild steel has never let me down, as I don't spend 5 hours a day grinding.
That's good news for you... get a suitable piece of *cold rolled* 1018 mild steel (or pretty much any steel will work fine) and make your own replacement.