  Recently, abstract argumentation-based models of case-based reasoning
($AA{\text -}CBR$ in short) have been proposed, originally inspired by the
legal domain, but also applicable as classifiers in different scenarios,
including image classification, sentiment analysis of text, and in predicting
the passage of bills in the UK Parliament. However, the formal properties of
$AA{\text -}CBR$ as a reasoning system remain largely unexplored. In this
paper, we focus on analysing the non-monotonicity properties of a regular
version of $AA{\text -}CBR$ (that we call $AA{\text -}CBR_{\succeq}$).
Specifically, we prove that $AA{\text -}CBR_{\succeq}$ is not cautiously
monotonic, a property frequently considered desirable in the literature of
non-monotonic reasoning. We then define a variation of $AA{\text
-}CBR_{\succeq}$ which is cautiously monotonic, and provide an algorithm for
obtaining it. Further, we prove that such variation is equivalent to using
$AA{\text -}CBR_{\succeq}$ with a restricted casebase consisting of all
"surprising" cases in the original casebase.
