I can't answer this as a midwife (yet--just got accepted to start in Vandy's CNM/FNP program in Fall 2014), but I've been an L&D nurse for 2 years, and have seen several demises.
Most of the demises I've seen have not been intrapartum--a woman comes into the office for her prenatal appointment, or into the office/hospital for decreased fetal movement, and there are no fetal hearttones. The few times I've seen midwifery transfers for fetal problems, the baby's been ok (and the close calls we've had have been a result of some weird clinical judgement by unlicensed midwives--for intrapartum incidents that threaten the fetus, I really think risk management and appropriate OB backup is paramount).
One of the hardest things about demises is not necessarily knowing what caused them. Like I said, most of the demises I've seen have been sometime in earlyish pregnancy (14-26 weeks), and several (but not all) of those babies are born with something grossly wrong--facial or torso deformities, noticeable edema incongruent with intrauterine decomposition, etc. Those are harder, because they're more disturbing to look at, but offer up some answers as to why the pregnancy wasn't viable (there was something wrong with the baby). Term demises are very hard (and less likely to be born with an unknown anomaly), but much rarer.
In all cases (intrapartum events or in-pregnancy loss), I think how the death is talked about is incredibly important--I always avoid using the term "miscarriage" when talking to the mom (it's not like if she'd somehow "carried the baby better", it would have lived), and while the idea of loss is often really helpful to discuss, I try to avoid "losing the baby" (like "We lost the baby" or "you lost the baby", because even in intrapartum events, everyone comes to the table with the best of intentions, and, one hopes, the best possible clinical judgement). The most helpful phrase (which I don't think I've ever been able to deliver without crying) has been "I'm so sorry this happened to your family."
There have been times when I've seen bad outcomes occur as a result of interventions in labor at the hands of OBs (vacuum injury once, but usually maternal morbidity)--as a midwife, I think it may be more likely that a bad outcome occur as a result of not intervening in labor (I say this because I think that's the bias in the respective professions, and because of what I've seen at work--like a far-too-late transfer). Those are always hard. There is no way around that--even if it's just a birth injury, rather than a death, or a relatively common-but-benign-but-weird-occurance (a broken clavicle on a not-shoulder dystocia), it's hard to look at the people you're taking care of and tell them that something's not perfect with their baby, and that you messed up and that is (or might be) the cause.
I also think that uncomfortable truth--that because we are human and make mistakes, and since we work in an industry where we work with people, there can be a very human cost for those mistakes--reinforces the need for a good clinical network. As a midwife, you want really excellent clinical judgement skills, and really excellent coworkers attending births with you or acting as backup--do you both think the woman's OK at home? Does she need that intervention? If you had to explain the case to someone else, what might they advise? 2 heads are better than one...and that also applies to the grieving process. It's good to grieve and talk shop with your co-workers--we all find demises hard in similar ways.
This has gotten so long, but a last thing: don't let fetal (or maternal--those are the worst for me) deaths keep you out of birth work. It's for sure one of the hardest things about this crazy, beautiful, super-awesome field, but in a lot of cases (such as when a pregnancy is lost early, when something is wrong with the baby), it's part of life, and your job is to handle that delivery and short-lived life with the same respect you'd use to deliver a term, healthy infant, and to help the mom on her pregnancy journey--wherever it may go. If midwifery is in your veins, this is too important! Go be an advocate for a ton of women, know that in order to do that well you have to have a good network, and know that sometimes that won't be enough to save a baby who's not going to make it (because of anomalies or illness)--I think that's the biggest hurdle to make peace with.