  We consider the two dimensional Schr\"odinger equation with time dependent
delta potential, which represents a model for the dynamics of a quantum
particle subject to a point interaction whose strength varies in time. First,
we prove global well-posedness of the associated Cauchy problem under general
assumptions on the potential and on the initial datum. Then, for a
monochromatic periodic potential (which also satisfies a suitable no-resonance
condition) we investigate the asymptotic behavior of the survival probability
of a bound state of the time-independent problem. Such probability is shown to
have a time decay of order $\mathcal{O}(\log t/t)^2$, up to lower order terms.
