  ${\mathcal PT}-$symmetric dimers with a time-periodic gain/loss function in a
balanced configuration where the amount of gain equals that of loss are
investigated analytically and numerically. Two prototypical dimers in the
linear regime are investigated: a system of coupled classical oscillators, and
a Schr\"{o}dinger dimer representing the coupling of field amplitudes; each
system representing a wide class of physical models. Through a thorough
analysis of their stability behaviour, we find that turning on the coupling
parameter in the classical dimer system, leads initially to decreased stability
but then to re-entrant transitions from the exact to the broken ${\mathcal
PT}-$phase and vice versa, as it is increased beyond a critical value. On the
other hand, the Schr\"{o}dinger dimer behaves more like a single oscillator
with time-periodic gain/loss. In addition, we are able to identify the
conditions under which the behaviour of the two dimer systems coincides and/or
reduces to that of a single oscillator.
