I talk with my clients about having a back-up come spell me if their birth goes really long. I have never had to do it, nor have I had to spell my doula-buddy when I have backed up for her. Personally, I think it's better to get a fresh horse, let the primary doula take a break and come back refreshed than to have three dog-tired people there when the mom might need somebody who can speak in complete sentences or be totally rational when she is not. Your presence is important, so if you can't be fully present because you are a walking zombie (or,heaven forbid, you get so tired that YOU start having contractions), it's better to hand off to another person who can give the couple the support they need.
I also have to disagree with Beccadoula - if you are prego., you need to decide beforehand how much you can do, and be up front with clients - maybe you need to take a break after 18 hours, not 36. Maybe you need to work in tandem with another doula or not take primiparas as clients, as they tend to have longer labors.
You will learn to do better phone screening as you go along, but it's true that some moms need support even with prodromal labor. If you go to them but things seem non-progressing over the course of a few hours, you can always talk to them about conserving energy, know this might be a long haul, tell them to do the bath and glass of wine routine, try to sleep, then say I am going home to rest also, but call me back if it picks up.
At the hospital, I take little breaks if the couple is in their own zone and don't seem to need me, but that means I sit on the couch and eat a snack if they are in the bathtub together, or I go down the hall to use the toilet and call my husband to check in with him. If the mom gets an epidural, I sleep when she sleeps, but again, on the couch right next to her bed.