x^2 + a^2 rears it ugly head again. If this can not be handled by one of the Mosek posters, it’s another candidate for @Erling’s convex modeling challenge Express 1/(a^2+x^2) in cvx
Note that in this case, with a, which is an input value (i.e., constant) suitably restricted, the function appears to be convex over the entirety of its domain.
BTW, your plot is not accepted on this forum as being a proof. I think it is convex for a >= 0.23, but I haven’t proven it.