Although the situation you describe involves amplification rather than homeostasis it is not a positive feedback loop under the standard definition of the latter:
In a a positive feedback loop:
An increase in A leads (directly or indirectly) to an increase in B.
The increase in B leads (directly or indirectly) to an increase in A.
This repeats step 1., leading to a further increase in B.
The second step is feedback, as it is affecting the initial propagator of the action, and positive, as it causes an increase in that propagator, A as well as target B.
Your model differs from this in two ways. First, only B is amplified — A is suppressed. Second, when A falls to zero B will reach a maximum, whereas in a positive feedback loop things theoretically keep on running out of control. (Yes they generally stop, but that is because of the intervention of something outside the simple A/B system.)
Some biological examples illustrate this difference (please, I am not concerned whether they are true or not).
An example of a positive feedback loop might be atmospheric warming (A) causing production of more water vapour (B) which has a greenhouse effect and increases atmospheric temperature (A), which...
An example of your model might be the territorial encroachment of smart and aggressive Homo sapiens (A) causes a decline in the population of H. neanderthalensis (B) which is then less able to resist Homo sapiens, leading to a further decline and eventual extinction of H. neanderthalensis.
At the end of the day, we are arguing about semantics. Your point of view would seem to be that the current definition of positive feedback should be extended to include your model. My point of view is that scientific terminology allows us to distinguish between similar but different things. So, (not meant as a serious proposal) one might include both effects under a broader description as ‘augmentative cycles’, including both the standard ‘positive feedback loop’ and your model, which could be called a ‘positive–negative feedback loop’ or a ‘terminal-positive feedback loop’ or whatever takes your fancy.
There is a paper in Current Opinions in Cell Biology which discusses the type of motif you describe under the subheading ‘Positive Feedback Loops’, although also refering to them in the text and in the title of a table as ‘double-negative feedback loops’. As @WYSWYG mentions, the review he originaly quoted only uses the latter term, and has a diagram of two-component regulatory motifs, which I reproduce below, distinguishing this from positive feedback. This bears out what I wrote — not that your point of view is necessarily wrong — but that this is a question of semantics, and scientists find it useful to use different terms to distinguish different but related things. In any case, the authors of the review have done the reader a service in defining their terminology.