苛 means harsh, exacting, small and persistent — the opposite of a single dramatic event. As a qualifier on 疾 it names the kind of illness that grinds.
The transmitted text is unsettled: the same chapter has 身無奇病 above and 苛疾不起 here, and some editions read 苛 in both places. The variant is recorded rather than resolved here, since the difference does not change the argument.