This has been playing on my mind since I read it, and I've done some searching. I've found a very long artilcle on causes and prevention of cot-death here:
https://www.familyrapp.com/Results/archive_results_details.asp?ArticleID=985
Feel free to read the whole article, but the main bit I found was this:
So what is the explanation for the rising rate of cot death from one sibling to the next? Cot death is caused by gases generated in mattresses - and many parents re-use mattresses from one baby to the next. If a mattress contains any of the chemicals concerned and fungi have become established in the mattress during previous use by another baby, generation of toxic gas commences sooner and in greater volume when the mattress is re-used. This accounts for the rising rate of cot death from one sibling to the next. It also accounts for the very high cot death rate among babies of solo parents, who for economic reasons are more likely to sleep their babies on previously used mattresses which they have acquired secondhand.
So I'm going to do what Hevz suggested and ask for vouchers when this one is born so we can get a new mattress.
Thanks to both Hevz and Hypnorm for bringing this to our attention.