Relevance of covariates?

I have a big group \(A\) of individuals that have one common characteristic that make them part of a study in which certain binary variable has to be accounted for. Logistic regression can be used in this case. This group of individuals can be separated in disjoint subgroups \(A_n\) based on the date they entered the study. When I perform logistic regression certain covariates appear to be statistically significant to explain log odds ration, but when I do perform the same analysis in each of the subgroups \(A_n\) most of the covariates that were significant globally are no longer significant, is there a good explanation for this?
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Omega Contributor
OR, when you run the sub-analyses the sample sizes are smaller and you no longer have the power to discern differences. Present the model outputs to better help us understand the results.