Because the generation time of the bacteria is very short, e.g. fractions of an hour, it is normal for the quantities of each kind of bacteria to vary during the day, following the fluctuations in the concentrations of various nutrients in the intestine.
For a constant microbiome composition, one would have to feed the mice with exactly the same food at the same hours each day, and sample the microbiome also at fixed hours that are the same each day.
Accounting for these covariates is important. But with larger sample sizes, they might cancel out anyway. IMHO, larger studies will be reproducible. There are other much more serious technical issues.