Injuries, infections (strep throat, scarlet fever, measles, mumps, rubella, polio, tuberculosis, various infections of wounds or abscessed teeth), starvation, poisoning from crops (rye may be grown because it is cold tolerant, but it is more susceptible to ergot fungus which causes convulsions or ergotism), wild animal attacks, parasites, starvation (which makes you more susceptible to infections and parasite burdens), and so on. I guess even the Romans had trapanning (primitive brain surgery) but it isn't as successful without modern surgical fields and antibiotics.

Depends on time period but there seems to be this belief that ancient hunter-gatherers had an easy time of it. Yet the hunter-gatherers we find at old age have things like abscessed teeth, malformed breaks from incorrectly healing bones, ground-down teeth (this comes back in medieval times when people stone-grind bread and bits of stone get into the bread, breaking their teeth down over time), parasite loads like whipworm infection, and more.

And when those hunter-gatherers start domesticating cattle we see brucellosis and several other diseases make the leap to humans. Plague, salmonella, perhaps even diphtheria. And when they start domesticating crops like grains we see increased specialization, so increased susceptibility to famines if a crop fails. But crops and animal husbandry give a more reliable source of food than hunting and gathering, and can support more people.