Does TCAS take into account aircraft performance/limitations when issuing RA's?
In theory, yes.
In practice, not totally.
i.e. inputs can be provided to tell TCAS about the config / altitude / conditions of flight. On the basis of these inputs, certain RAs can be inhibited. (and these inhibitions are data linked to the threat aircraft as well, for the purposes of coordinating the RAs generated.
However, these inputs may well be fairly gross, and not be comprehensive enough to prevent an unachievable RA. E.G. airframe icing, engine out. Sometimes they appear just plain optimistic. But bear in mind that RAs should not be long duration. In a coordinated encounter you should not even need to maintain the adjusted rate until CPA. Unless the other aircraft is doing something dumb, all TCAS is doing is shifting your flight path up or down a few hundred feet, we are not in the business of long duration climb demands.
It would be interesting to know the cause of your spurious RA. Ultimately, TCAS does not directly protect the flight envelope. Every TCAS manual I've ever seen has warned that the flight crew must protect the flight envelope, although admitably its been a few years since I was directly involved.
pb