Oh, this is going to be touchy.
Let's be clear on one thing right now: early Stoics advocated suicide. They felt that, if you live in a situation that will most likely never get better, taking your own life was the way to go. Cato did this when, knowing that Caesar took power, took his own life. He knew Caesar wasn't going to let him get away with opposing him.
Seneca devoted an entire letter to the subject. In letter 70, he writes that the wise man “...will live as long as he ought, not as long as he can.” He continues. “As soon as there are many events in his life that give him trouble and disturb his peace of mind, he sets himself free.” Seneca didn't think we should hold to hope (such as in the events of a terminal illness or even prolonged entrapment) because often we pay more to stay alive through hope than if we ended it. Even more, even though he felt we should endure illness and pain bravely, he felt that to endure endless pain was foolish.
Yikes. So, now that times are a bit different, I think it's time to take another look at this subject. Stoicism, after all, changed with the times when it needed and yet kept it's core values. And we, as philosophers, should challenge what we don't agree with, if we are able to. And there certainly enough here for me to disagree.
I'm going to start off by saying I'm not totally against suicide in all situations. I do think that those with terminal illness, nearing end-stage, should have the right to skip over the pain they might have. Having said this, I don't necessary think we should end our lives.
What is the goal of living our lives with Stoicism? It's like the archer Epictetus talked about. The Stoic archer shouldn't concern themselves with hitting the target. They should worry more about making the best shot they can. After all, a sudden gust of wind, a cough, anything can ruin our chance of even landing a hit, let alone a bulls-eye. We'd laugh or even admonish the archer who'd let a screw up cause them to quit.
For me, life goes the same way. We all have death as the end, with a good death (a virtuous one, that is) being the “bulls-eye”. Sometimes, we have these screw ups, like bad breakups and other short-term problems to long-term problems like chronic illness. But, like the archer above, we'd be foolish to quit simply because something happens to us and, perhaps, keeps happening to us. It's all about taking the best shot possible each time.
To base it off William B. Irvine's words, we need to act as the best person possible. Sometimes, that means acting like the best person possible with chronic pain, or cancer, or mental illness. Sometimes it means acting like the best person while trapped in prison or in captivity. If it's, as the Stoics say, possible to live virtuously in all this and worse, why should there ever be a need to kill ourselves?
Let's go back to the terminal illness case. Certainly, I could live virtuously in a situation like this. I can still carry on my duties as a husband and a father. But I can now also serve another purpose: by being a role model for others suffering. I could also make it my duty to raise awareness or give to charity. In short, even the worst of situations do not mean I'm diminished in anything expect for some possible indifferents.
Sure, perhaps some could argue that some people aren't strong enough to carry on. And maybe this is true. But if we keep in mind that a good life leads to a good death, I think a lot more people might be more willing to change their thoughts on ending their lives. Especially when we consider that what enjoyment that comes from our lives comes not from external events like our bodies but internal. We don't need to be healthy or physically free to experience the Stoic joy. And, in knowing this, I can't ever see a reason to end our lives before our time.