Attempting to reconstruct Roman mortality rates is extremely difficult, especially considering how long the period and how wide the geography we're looking at. So: although some work can be done with tombstones and cemetaries, we need to bear in mind that not all people were commemorated in the same way at the same time - the epigraphic data has a tendency to swing from showing an excess of young adult mortality to everyone apparently dying of ripe old age. It's generally accepted that using epigraphic data underestimates the mortality rate in the very young and the very old. So far, so useless for our purposes. Likewise, the skeletal remains are biased in different ways, from difficulties in aging adult bones to Rome not likely having a stable population which statistical models can be employed on. Frier takes the approach of using census returns from Egypt in the first three centuries CE to reconstruct mortality, and although it would be extremely useful to have more data and especially more data on the whole of the Empire, this is likely the best shot we have.
It's plausible that the most common cause of death inside Rome itself was disease, especially in the summer months when malaria was rampant, something the wealthy left to avoid. Much of the city lived in extremely crowded conditions in what were essentially blocks of flats, where it was impossible to avoid close contact with other people. Likewise, although fresh water was free and available, it may have been contaminated with waste, animal corpses, etc. and have helped to spread illnesses like typhoid. Disease is an equal opportunity killer and gender likely did not play into which people died of this most common cause. This was probably less common outside of Rome and other urban areas, which were likely mortality sinks relying on immigration to maintain population, but still a significant factor.
However, the second most common cause of death was likely to be is childbirth, mostly for the infant. Recent scholarship on infant mortality suggests that approximately 3 in 10 may have died in infancy, and it is likely that approximately 25 in 1000 labours lead to the death of the gestational parent. There's - unsurprisingly - a great deal of anxiety recorded in early imperial Rome about producing children. Although it's possible that there was some level of femicide practiced in terms of infant exposure, we do not have any data to prove this, and it does not seem to be reflected in Frier's demographic tables, suggesting that at the very least it wasn't happening in Egypt.
So these two primary causes of death are for the most part not gendered, and although looking at Frier we discover that although women are more likely to outlive men, it is not a particularly dramatic imbalance. It also seems to be fairly similar to demographics in India and China at the beginning of the 20th century, which suggests that the data is solid. Altogether, this suggests that there was largely no sex imbalance in the Roman Empire or that there was an excess male death rate, and that in the normal course of things women would have had little difficulty finding a husband. Obviously, this is not applicable in all places at all times; certain events such as the Second Social War would have had a dramatic (but temporary) effect on the numbers of men available to marry, in an event not unlike the "surplus women" after WWI in the UK. Although there are often concerns about marriage, particularly notably Augustus' moral laws, these do not seem to have been motivated by women not having potential partners, but rather to force people who were not marrying into doing so and having legitimate children. They apply more-or-less equally to everyone, and penalise those who don't have children and reward those who do.
Sources: Frier, Bruce W. "Demography" (2000), in Alan K. Bowman, Peter Garnsey, and Dominic Rathbone, eds., The Cambridge Ancient History XI: The High Empire, A.D. 70–192, (Cambridge: Cambridge University Press, 2000), 827–54. Parkin, T. G. (1992), Demography and Roman Society Schiedel (2009), Death and Disease in the Ancient City of Rome, Princeton Shaw, B. D. (1991) ‘The cultural meaning of death: age and gender in the Roman family’, in The Family in Italy from Antiquity to the Present, eds. D. I. Kertzer and R. P. Saller. New Haven: 66-90. Todman (2007), Childbirth in ancient Rome: From traditional folklore to obstetrics, ANZJOG