If the probability of a bad measurement is small than the probability of having two bad measurements out of three will be very small, thus neglecting the outlying one among the three will usually leave you with two valid measurements.
I would, however, record all the values measured, even other measurements on the same subject/sample. On the strength of a data collection of valid and bad measurements you could study the distributions of bad and valid measurements. You might also see that bad values depend on the true value (and thus carry information) and both bad and valid values may depend on other measurements of the same subject/sample. When you possess the (conditional) distributions of bad and valid measurements, and the proportion of bad measurements then for each specific measurement you will be able to calculate the probability that it is bad (comes from an other distribution), and to calculate best estimates and established confidence intervals.
I believe that your protocol (keep the two if CV is low, otherwise use the lowest CV pair of three) may be good to start with, but I would revise it after collecting enough data to know more about bad measurements. However, whether a protocol is acceptable also depends on the probability of a bad measurement, how bad a bad measurement is, and how critical is a bad best value in its application.
I assume that you are talking about CV because you analysed some of your existing data and you found CV to be stable. This suggests that measurement error is proportional to the value, thus measurement error SD is constant on the logarithmic scale. If so, taking the geometric mean (not the arithmetic mean) may be more accurate.