I think that Fritz Maurer and Countryman have it right. I suspected that the thickness might have been the issue, and based on countryman's experience, the casting is too thin. They want to keep it light, but conflicting requirements lead to compromises. If it is too heavy no one will buy one and if too light no one will buy a second one.
There is a post from another forum below. Someone used a 1/2 in. (6.2 mm) carbon steel plate and measured a 0.020 to 0.025" (~0.5 mm) thickness loss after 15 years in a wood stove. I would expect the the more rapid heating of a much thinner sheet would cause more loss.
Countryman's comment about decarburization is interesting, since cast iron has about 4% C while mild steel has only 0.2% C, but the temperature given for decarburization might be centigrade, not Fahrenheit, and the amount of oxygen is important. A fast burn with the damper wide open would cause more oxidation than a damped down burn. That is not saying he's wrong, it's just complicated. On the subject of burning, I like the manufacturer's excuse about burning pine. Hardwoods burn hotter than pine. If the pine is making soot and creosote, the oxygen content and temperature of the combustion gasses would be low. I guess they felt that telling you not to use hardwood would have been too obviously a load of bull manure.
Regardless of which steel you buy, it seems that thickness is your friend. Any carbon steel will work, but not quite as well as stainless. Any of the 18-8 stainless grades (301-305) or 409, which is used for car exhaust systems should be fine here. Performance will be about a wash between any of them, so price and availability are the main drivers. 409, if you can find it, is a little better. It appears that 1/8" of cast iron is too light, and 1/2" carbon steel plate is overkill. My guess, and it is only a guess, would be a minimum of 1/4" cast iron, 1/8" (10-11 gauge) carbon steel and just over 1/16" (14-16 gauge) stainless steel.
For the record, Fritz thinks in metric, and 3 mm is 1/8 inch. 6 mm is closer to 1/4. So yes, too thin, but 1/8 inch for those of us who think imperial. Not easy to think in both systems at once. I disagreed with Fritz based on the assumption that he is translating between metric and imperial and thinking that 1/4" wasn't working. I could be wrong.
Hardox, as stated before is a brand name AR steel. Almost exactly the same stuff as some armor plate, minus the expensive ballistic testing requirement. Hardness and wear resistance are closely related. AR steel contains maybe twice as much manganese as mild steel. Mn is also good for wear, but doesn't do anything for oxidation resistance. Pretty much the only thing to look for in a low alloy steel is the thickness.
https://app.aws.org/forum/topic_show.pl?tid=11829 is a thread asking the same question. The good answers were:

By MDG Custom Weld
Date 05-14-2007 16:48
We have repaired wood stoves in the past, and here are some things to keep in mind:
1. Clean and prep the steel as much as possible to remove any soot/ carbon build up. This is really important if you're welding in any type of stainless steel.
2. Remove the stove from the home or where ever it's at if at all possible. A spark in the flue can cause a fire if it lands on some built up creosol
3. Most inside stoves are made from carbon steel plate.
4. If you're welding in some ferritic SS, we always use 409 plate with 409 metal core wire.
5. USE CAUTION!!
and
By fbrieden
Date 05-14-2007 18:52
Replaced mine with 1/2" A 516 Grade 70 about 15 years ago and a UT test on it at several locations came in at .475-.480 (after power brushing). The baffle is lasting longer than the refractory bricks that I have to replace again.