Should I remove 0 values from my dataset if they seem to be from instrument error? I have conducted an experiment looking at the decay rate of a DNA target in flowing water over time, with 4 replicates of each treatment. The data is collected via dPCR Quiacuity instrument that calculates well concentrations (gene copies/uL) based off of positive and negative plate partitions. At some time points (seem to be random), 3 of the replicates will have a given concentration closely matching one another (similar amount of positive partitions), but the 4th is equal to 0 (no positive partitions counted fluorometrically at all). Since the other concentrations have little variance, this leads me to believe that the 0 data point was from instrument error. My issue is that this 0 drastically changes the slope of the regression (log-linear, x = time, y = LN(gene copies/mL) compared to the others within its treatment, making it difficult to confidently statistically analyze them as a group of replicate regressions. I will end up re-running these specific samples to ensure this is the case, however, for now is it okay to remove these 0's and calculate the regressions using datapoints that I'm certain are valid?

Firstly, good on you for asking this question --- too many analysts think they can remove "outliers" merely because their statistical models are not dealing well with those observations.  Such an attitude asks reality to conform to the limits of the analyst's statistical knowledge, rather than asking the statistical methods to adhere to reality.  The fact that you are asking this question shows that you have an awareness that you cannot discard data just because it is affecting your statistical model in a way that you don't like.

Presumably the ultimate goal of your analysis is to learn about the decay rate of DNA, not the secondary phenomenon of instrumental reaction to this.  Consequently, if you have good reason to believe that an aberrant data value is from instrumental error rather than a genuine absence of DNA decay, it is not only legitimate but desirable to show your reader what would happen if you remove that data point.  (In some cases you might consider ditching all your data and running your experiment again more carefully, but I'll leave that aside for now.)
If you're not sure whether this data value is "genuine" or not (i.e., whether it reflects an underlying value of the DNA decay or instrumental error) then a prudent thing to do would be to show your regression results under both scenarios, though you might relegate the one you think is less important to an appendix or supplementary materials.  You should also explain to your reader why you believe that the aberrant data point is from instrumental error.  Obviously we cannot tell you whether or not your aberrant data value was caused by instrumental error or not, since that would require more experimental context and field-specific judgment.
Finally, it is worth noting that detection instruments sometimes have some kind of minimum "threshold" required for them to "detect" the thing under consideration.  In such cases you get a form of "censored" data and there are statistical methods that can be used to deal with this data.  Again, this requires field-specific judgment and knowledge of the instrument to diagnose, but it is worth considering.
