It is not clear if the metal or the plastic around the wire is deteriorating.
If it is the insulation, make sure you buy high temperature wire. The insulation will be good to way above kiln temperatures. There are usually a Teflon coating.
If it is the metal part of the wire, then you might consider marine grade wire. The strands are tinned for corrosion resistance on this wire. It is probably sold by some other name too.
If it is the connections corroding, consider soldering and crimping, then covering this with a silicone sealant, maybe with heat shrink around it, to protect it from the moisture and acids.
If the problem is from wire flexing - so mechanical damage - consider adding some type of strain relief so all the flexing does not occur in one spot. You might be able to build this up with heat shrink, but there may also be something off the shelf.
Sorry if this does not help - I have not seen exactly what the problem is.
As always, you should ask the manufacturer. They are always willing to help and have an interest in seeing their products perform well.