I'm working through Mike Duncan's "History of Rome" podcast, and people in it seem to commit suicide extremely readily - whereas we would consider it an absolutely worst case scenario.
Is this true, and if so, why was this? Was exile so bad, or fleeing to a neighbouring empire out of the question completely? Did they have stronger religious convictions? I've heard "honour" was so much more important, if so, how and why?
It's the one thing that makes the least sense to me, I'd love to hear some reasons for this.
It depends on who you are talking about. The Romans did consider suicide a good way to go if a person was going to die anyways (this is best shown in Pliny's letter 3.16 about Arria and Paetus). However, depending on the person, there might be other reasons for suicide. The proscriptions under Sulla and the maiestas (treason) trials under the early emperors lead to a lot of suicides because the state would confiscate the property of anyone found guilty (and they found most of the accused guilty). If you killed yourself before trial, your family could keep the property.
During the republican era a ritual existed to try to change the course of a battle. The general would vow himself to the gods of the underworld and rush into enemy ranks. The act of Publius Decius Mus would later be remembered by one of his grandson while he was losing a battle, he felt obligated to do the same.