In case of an unbalanced number of samples per group, the standard DESeq outlier replacement (minReplicatesForReplace=7) can result in drastically reduced p-values. This happens when the trimmed mean replacement leaves out all samples from the smaller group. See the following example:
First two values belong to the smaller group. The last value (larger group) is replaced by 154:
1272, 751, 275, 298, 113, 116, 161, 176, 294, 172, 327, 93, 108, 84, 151, 728
I am aware that unbalanced groups and small sample numbers should be avoided, but this happens quite often in reality ;-). I would prefer having the outlier replacement deactivated by default or a check for unbalanced groups...
moved comment to answer below
You might want to experiment with edgeR's quasi likelihood framework to mitigate the affect that outlier observations have on your differential expression statistics.
Given that you're looking at a very specific use case and have observed specific instances of behavior that might not be ideal with your current workflow, it would also be interesting and valuable to the community if you tried this and come back with a report of your findings ;-)