From what i can tell, the "burning" of the fuel should only produce water and carbon dioxide, assuming that the fuel is relatively pure, because i could only find hand warmers that burned naphtha or LPG, both are mixed hydrocarbons. So with that in mind lets try and attack it logically.
Please bear in mind that im not a chemist
So, if we have 2 waste products: water and CO2, how do they make the pad degrade?
It could be that the substrate (the thing that the platinum is impregnated in) is hygroscopic, and absorbs the water from the reaction. This is my best guess purely because it would stop moisture building up in your pocket and allows them to sell more pads.
Its possible that the C02 could dissolve in the water to make a weak acid, and that makes some interaction, but i would err towards that not being much of a contributing factor.
So, with that in mind, what can be done to stop it?
You could try and use a powerful desiccant to extend the life of your pads. Adding a powdered desiccant should absorb at least some of the water and therefore increase the life of your pads, you may even be able to to add some dry crushed silica gel to the top of the pad. The problem with that though is that the substrate is much more efficiently placed to absorb the water, so it might not be that effective.
If the water is indeed the issue though, you could take some of you old pads, and separate the platinum (try burning at a low temp followed by an organic solvent). That should leave you with colloidal platinum, carbon, and some ash (from the unknown substrate). Try impregnating various other substrates with that, perhaps with your own desiccant.