I do rentals out of my excess, so I'm not super hard-nosed about late fees, especially if I know they had a legitimate emergency. If they get all casual about it, then I'll start requiring it. It sounds like you are getting there, especially as this hospitalization seems to have effected their timing on paying the rent, but not their ability. As for eviction, my rule is usually two months behinds, just because at that point it is cheaper to just move than to pay the current landlord.
Another thing to consider is getting them set up on auto-draft, if this is truly just a problem of "forgetting". Maybe ask them about that in the discussion on future late fees.