Obviously they weren’t able to deal with serious illness the way we are, so something that might be minor and cleared up easily today might kill someone in the ancient world. But no, I don’t think they were kind of sick all the time.
We hear about plagues - the Periclean one, the Antonine, etc. - and we certainly hear about individual illnesses both in history/biography/fiction and medical literature. As mentioned above, malnutrition would definitely have been common. One can’t prove a negative, and maybe they were sick all the time, but I’ve never seen any evidence (and we do have a substantial amount of information about daily life among elites) that there was a sense they were sick all the time.
On her wedding night, my Grandmother’s mother told her that on *her *wedding night her mother had told her that she would have eight children and four of them would die. And she had been right.
I think it’s important not to lump all people from more than a century ago under the category of “ancient.” The normal health of an urban Hellenistic Greek was not that of a Mesolithic hunter-gatherer or a central Asian pastoralist. Even within cultures there was tremendous variation by class, age, sex, and so on. It makes it well-nigh impossible to generalize about all dead people (also known as Pastos and Oldendayzers). With that said, there are a few things that are generally true of most cultures:
Speaking as someone who has looked at the teeth of lots of deadies, I can say that if you regularly ate some sort of ground starchy meal, your teeth would be worn to varying forms of smooth nubbins by mid-life. This includes a lot of cultures that didn’t have agriculture but who relied on a staple food that had to be ground (such as the Chumash Indians with acorns). Until sugar and super-refined carbohydrates (white flour, I’m looking at you) really became common foods a few hundred years ago, cavities or obviously rotted teeth were relatively uncommon.
It’s not much of an exaggeration to say that everybody had a veritable smorgasbord of parasites (intestinal roundworms being particularly ubiquitous), and that most people in most cultures were swarming with parasites by modern western standards. Depending on the individual and the severity, parasites could have effects ranging from mildly beneficial (in terms of immune systems) to, well, death. A lot of people, perhaps the majority, had their health worsened in some way.
Having lots of nasty viral and bacterial diseases floating around was not ubiquitous. That is an artifact of sedentary societies, particularly urban societies, and also particularly in regions with relatively high population densities. There’s a reason why we gave the native americans smallpox and not the other way around; Europe and Eastern Asia, and the connections between the two, were what gave rise to the great and mighty communicable diseases.
And then of course there’s starvation and malnutrition. The distribution of evidence of periodic starvation in the form of linear enamel hypoplasias (dented bands on teeth) was not at all uniform between and within societies. In the classical world, for example, slaves were more likely to have hypoplasias but but they were relatively uncommon among free people. Neanderthals almost invariably had several, indicating repeated periods of starvation very early in life. So depending on who and where and when you were there were a lot of people chronically malnourished.
Andrew Hull Foote, a gunboat admiral in the US Civil War, scraped his shin on a gunwale (plank of wood) in a launch (small boat). He subsequently died of the ensuing infection from this minor and common sort of boo-boo.
Jack and Jackie Kennedy had a newborn son in August 1963 who died of hyaline membrane disease; he would almost certainly have lived, had he been born today: Patrick Bouvier Kennedy - Wikipedia
I, and most of the people I know, would be dead today if not for the availability of modern medicine. In ancient times, many died in childhood and few lived past age 30. Even up until a couple hundred years ago, quite a high percentage of females died in childbirth. Check out any old graveyard and you’ll see evidence of this.