So a trend I've noticed a lot of with Roman and Greek leaders is that many of them seem to go through a lot of wives however there is usually not a lot of information mentioned as to why.
Was there any reason for this? Perhaps a lot of childbirth deaths? Maybe political divorces and remarriages?
In the Roman example political divorces and remarriages couples with lax divorce laws. In a cum manu marriage the woman was placed under the legal control of the husband. He had full control over her and could, once he gave the dowry back to her father, get rid of her at will. Divorce was really easy, especially for Roman men.
Part of the implicit marriage contract was that the two people would have a respectful relationship and make babies together. Once this was no longer the case divorce might soon follow. For instance, Claudius disposed of his first wife Plautia Urgulanilla on suspicion of adultery. Julius Caesar got rid of his second wife Pompeia for the same reason.
As you mentioned child mortality was high and it was not uncommon for rather old men to remarry to a much younger woman. For instance Pompey married his fifth Cornelia Metella after his fourth Julia died in childbirth.
Political expediency also played a great part. Claudius disposed of Messelina (wife 3) because she attempted a coup and married Agrippina (his niece) to cement his dynastic ties within the Julio-Claudian family.