  Parity-time ($\mathcal{PT}$) symmetric systems are classical, gain-loss
systems whose dynamics are governed by non-Hermitian Hamiltonians with
exceptional-point (EP) degeneracies. The eigenvalues of a
$\mathcal{PT}$-symmetric Hamiltonian change from real to complex conjugates at
a critical value of gain-loss strength that is called the $\mathcal{PT}$
breaking threshold. Here, we obtain the $\mathcal{PT}$-threshold for a
one-dimensional, finite Kitaev chain -- a prototype for a p-wave superconductor
-- in the presence of a single pair of gain and loss potentials as a function
of the superconducting order parameter, on-site potential, and the distance
between the gain and loss sites. In addition to a robust, non-local threshold,
we find a rich phase diagram for the threshold that can be qualitatively
understood in terms of the band-structure of the Hermitian Kitaev mo del. In
particular, for an even chain with zero on-site potential, we find a re-entrant
$\mathcal{PT}$-symmetric phase bounded by second-order EP contours. Our
numerical results are supplemented by analytical calculations for small system
sizes.
