The F-Test fails if the deviations between the predicted observations and the mean observations become too large. Since any model is just an approximation of reality, it would be unreasonable to expect all the mean observations to lie exactly on the model curve. If the variability of replicate measurements is moderate, the denominator of the critical ratio is large enough to absorb this effect, and the test performs as desired.
However, due to advances in assay design and execution, modern assays will often exhibit very low replicate variability. These advances in measurements precision aim to improve the assay precision and to reduce uncertainty of the result, but also reduce the denominator of the F-Test. For these assays, where the denominator of the test statistic is very small, the test may become overly sensitive and start failing assays that show no apparent flaws.
The following example illustrates this point. First, let's have a look at a sample with high variability in the replicate measurements. Judging from the plot, the sample looks acceptable. Since the predictive error is low in comparison with the high replicate variability, the sample passes the F-Test.