... i.e., why was the birth rate so low?
Are there any parallels with lower birth rates today?
One theory I found blamed hot baths:
If the Roman baths were hot enough to cause fainting and fatigue, they were probably hot enough also to cause chronic low fertility among males.
That article seems to be supposing that A) there was a decline in the birth rate at Rome and B) that bathing habits alone are enough to explain it. One wonders why other bathing cultures, such as those in Japan or Finland, in which hot baths or steam saunas are not only common but more or less a daily activity, do not have similar problems with chronic infertility.
There's a great debate currently regarding the decline in the citizen population in the late Republic. The crux of the debate rests with Ti. Gracchus, but it's one that remains relevant throughout the late Republic, since the loss of the citizen population was identified as an issue several times over the the course of Roman history. The issue here is that the decline in citizens supposedly identified by Ti. Gracchus does not in fact seem to hold water. The census figures in Livy and his Periochae show a general decline between 164 (337,022) and 131 (318,823). However, at the next census in 125, following the land commission set up by Ti. Gracchus, there's a massive jump to 394,736. That increase is far too high to be explained by birth rates alone, and has led to two opposing schools of thought, the so-called "low-counters" and the "high-counters." Both schools of thought suppose that the census must have been quite inaccurate, but diverge in their opinions of just how inaccurate it was.
The low-count supposes that the Republican census, though inaccurate in its details, was able to capture broadly the Roman citizen population in Italy, and that the decline we're seeing here is due to some other factor that resulted in fewer people reporting themselves to the censors, such as an unwillingness to fight unpopular wars or something. Following Ti. Gracchus' land commission there was an incentive to register, in order to be eligible for the distributions of the ager publicus, and the census jumps up sharply. Alternatively, we know that from one census to another the censors were not necessarily as diligent as their predecessors, to the point where many census were not even completed. We may well be looking at two very overzealous censors in 164 and a string of less devoted censors until 125. The high-count, which is really just Lo Cascio at this point, suppose that the census was never more accurate than 55% and that in fact Italy had nearly twice the population represented in the census. Not many people accept the high count, however, and the evidence is poor. There are also a few holdouts like Keaveney who dismiss the census data and insist that the texts must be correct and that there must have been a decline in the citizen population.
What is certainly clear is that, taken together over time, the census figures show an obvious increase in the citizen population that is consistent with exponential models. Most surveys of this sort of thing only restrict themselves to the second century because they're interested only in the Gracchi, and the changes in the census and the citizen population after the Social War and Augustus screw things up a little bit, but what we see is an overall steady increase in population. This seems inconsistent with the view commonly expressed in antiquity that the citizen population was always in decline. It is true that in the city itself the rate of death to disease was, by even the most conservative estimates, about even with the birth rate, and that the city's population was constantly being fed by immigration from Italy. However, overall this does not seem to have been the case.
As far as I'm aware (although I mean I'd have to go through the historiography to be sure, it's not quite my field) those who reject a decline in the citizen population, as I think (and I would be inclined to say, off the cuff, the majority of scholars agree) we must, would rather explain Augustus' marriage laws with his general appeal to Roman morality and to the deprivations suffered by the senatorial class in the civil war. The Augustan marriage laws and laws on childbearing and so forth were part of a larger program of "restoring" (or perhaps "establishing," depending on whether we think it was there already) Roman morality. Our texts repeatedly emphasize Augustus' horror at the lack of lasting marriages and the cavalier attitude with which the senatorial class in particular supposedly understood their moral place in society. I'm not sure why we should necessarily throw the testimony of our texts on this point out. Even if we suppose that much of Augustus' outrage was political, intended to present himself as the moral savior of the city, the volume of laws of this sort passed, many of which were of questionable popularity at best, seems to go far above and beyond mere rhetoric. Moreover, just as it's been suggested Ti. Gracchus might have extrapolated the situation of Italy incorrectly from a small sample size in Etruria (which, despite what our texts say about the incident, seems contradicted by the survey archaeology in Etruria), Augustus may well have misunderstood the general trend with a local trend. When Augustus passed his laws on marriage and births the Roman state had suffered from a decade of nearly continual civil war, preceded by a further half-decade or so under Caesar. The immediate loss in citizen life and property were immense. We know that the losses of the civil war were at least identified by contemporary Romans as having demographic effects on the population, since authors like Horace mention that there aren't any young men in Italy anymore because they're all dead. Just as in the decades immediately following the Second Punic War we see a drop in the census figures that then fairly quickly recovers, we should expect a similar effect on the Roman population during the civil wars. Unfortunately the census was highly irregular until Augustus, and our population data for the latter half of the first century are not great. Still, we do know that particular segments of the population--those, incidentally, most heavily targeted by Augustus' moral bills--had suffered particularly heavily. The senatorial class had been decimated by the civil wars, and though expansions of the senate by Caesar and Augustus served to keep their numbers up these senatorial introductions were more often than not not from the "old nobility," senatorial families of great and ancient reputation. Between civil war and proscriptions the nobiles, those with consular ancestors, suffered heavily, and the patrician order in particular (a minority even among that minority), which was on its last legs already in Caesar's day, had all but ceased to exist. Augustus tried to rectify many of these problems by, for example, promoting senatorial plebeian families like the Gracchi's gens Sempronia to patrician rank, and the marriage laws appear to be of a similar vein. The patrician order, with its narrowly-defined entry by heredity, had long lost ground to the plebeian senatorial nobility, and had been bleeding to death for centuries--the OCD remarks that of 50 or so patrician clans known at the beginning of the Republic, only 14 still had surviving patrician lines by Caesar's time. The precise mechanics by which the patrician order died out are unclear. Cases of transitio ad plebem occurred, but appear rarely in our sources. Likely a lack of suitable marriage partners forced many to marry into plebeian noble families or to remain childless (or adopt), and over time the order simply died out--the effect of the civil wars must also be mentioned, of course. I believe it's Tiberius who lamented the lack of patricians available for the priesthoods that only they could hold, and the greater lack of patricians willing to contract the archaic and restrictive marriages that were necessary for appointments like the flamen Dialis. It would seem, then, that Augustus was identifying a short-term population decline, particularly within a relatively small group of the population, when it seems that broadly there was no great population decline