The analysis assumes that the each observation is a separate experimental run. If the outcome of one run is measured more than once, then the average measurement should be used. Otherwise, the measurement error serves as the experimental error. You would, in fact, have two levels or random effects.
In your case, you actually replicated each run 7 times, so each observation includes the necessary necessary random error for the modeling. I would enter all 8 runs for each treatment.
The failed runs should be omitted. Just leave the response as missing in these cases.