  We investigate the effects of a time-periodic, non-hermitian, PT-symmetric
perturbation on a system with two (or few) levels, and obtain its phase diagram
as a function of the perturbation strength and frequency. We demonstrate that
when the perturbation frequency is close to one of the system resonances, even
a vanishingly small perturbation leads to PT symmetry breaking. We also find a
restored PT-symmetric phase at high frequencies, and at moderate perturbation
strengths, we find multiple frequency windows where PT-symmetry is broken and
restored. Our results imply that the PT-symmetric Rabi problem shows
surprisingly rich phenomena absent in its hermitian or static counterparts.
