Self-selection bias during the course of experiments
Apparently this is called attrition bias. It's very similar to survivorship bias. This paper suggest correcting for it using Heckman correction. Propensity score matching may also help somewhat. My experience with both has been mixed, but they are commonly used. You should figure out what exact approach is most appropriate for your setting.

One last edit: These two papers, which talk about bounding the average treatment effect, may also be of use to you.