This problem is pretty much universal with many factory headers; not just the mx-5. The stock construction is not very resilient for being so close to the exhaust. For example, in 2002 when nissan first implemented these header cats, they would suck up the chunks even on factory cars--and chew up the motors as a result! Luckily with the MX-5 they either melt or turn to powder and get ejected out the rear. For street use and what the EPA dictates it works, but put them on track or really romp on them with forced induction and their life expectancy shortens significantly. You don't see track cars running cats for this reason, and the race cats with the more durable substrate, are still wear items as Brian says above and their lifespan will depend on use. Poor tuning, NA or FI, will kill them as well and why we have always offered the datalogging/revision free of charge.
With that said, feds mandate that auto manufacturers cover emissions 8 years/80k regardless of warranty period, though I'm not sure if they would honor that knowing the car was used on the track or if they saw a supercharger bolted on
If you go to auto-x events around here you'll find many subaru and evo drivers with masking tape on their plates for this reason!
Tuning for the cat itself is a whole other issue. It is a delicate balance because if too rich, the unburned fuel will decrease the overall life of the cat. Though cats survive at 14.7 AFR and high temps at cruise, do the same thing under high load and they melt if it is prolonged--this is a bigger priority. So it is a delicate balance in reducing risk of meltdown, while optimizing the life of the cat by keeping it from being too rich. For a street car this could be done without increasing emissions; but for track use, particularly with forced induction, it is a bigger challenge.
If you look at the factory mapping you can see how they adjusted it for maximum converter life in regard to fuel--very delayed open loop transition (keeping stoich as long as possible), lean AFR in the midrange (13.5) tapering to 12.2 or even 11.8 by redline to keep it cool for prolonged runs. Terrible for power everywhere except 5000-6000 RPM!