I have not closely studied Derrida’s critique of Agamben from The Beast and the Sovereign, yet given how frequently it’s been deployed by Agamben skeptics, I feel comfortable giving a brief, blog-style response to it: that bios and zoē cannot be neatly distinguished does not undermine Agamben’s project, but is indeed the entire point.
Agamben reads the Western tradition as a series of increasingly destructive failed attempts to separate them out in some kind of stable and sustainable way. The reason these attempts fail is that the neat distinction is impossible — indeed, even in the encounter between the sovereign (the very embodiment of bios as political life) and the homo sacer (the emblem of zoē as bare life), which should surely count as the starkest possible contrast between these two concepts of life, an uncanny overlapping occurs wherein both are included through their very exclusion.
Agamben is thus not trying to get rid of bios in favor of a pure zoē — i.e., to abolish politics and allow us all to return to our raw animality or unblemished nature — but to get at another politics, another form of life that would not be governed by this founding opposition of the contingent historical reality that is Western politics.
There is doubtless a lot to be said in critique of Agamben’s project, but Derrida’s critique misses its target as far as I can tell.