What does detection stability mean?
Detection stability is about consistency of detection, in this case rare events are classified independent of small changes. One might think of detector having smooth function when it is stable and chaos-like, heavily discontinous when it is not.

Detection stability in the case of rare events (rare attacks) is about consistency and fluctuation. The lack of stability means that similar events, that differ marginaly will not be detected, becase the techniques are very prone to fluctuations - that is a very bad property, malicious query with e.g. $99\%$ classification when changed slightly might drop below detection threshold. Another outcome is that slight changes to the rest of population will influence rare queries.