Estimating stability and mean life of anomalous tautomers
TLDR: With a quantum/semi-classical transition state theory.
I order to determine the lifetime of the tautomer, you need to know the rate constant for the decay from the tautomer to the conventional dimer.  This is a kinetics question rather than a thermodynamic question so you won't be able to answer this by comparing single point DFT energies.  The rate will also vary with temperature.
A complicating factor is that the nuclei moving are protons in hydrogen bonds.  Hydrogen bonds are frequently double well potentials with two minima, one near each end of the bond - in this case the tautomer and conventional dimer.  In these case the physical distance between the minima is small and the proton may tunnel through the potential barrier between the two minima - hence nuclear quantum effects are likely to be important, at least at low temperatures.
Methods that can calculate nuclear quantum effects can be very computational expensive and may require you to work in a reduced dimensional represention - only considering the two protons quantum mechanically and potentially simplifying the surrounding structure.
Two potential methods that could calculate a rate taking account of nuclear quantum effects are  semiclassical transtition state theory, or ring-polymer molecular dynamics which has been applied within pockets of larger systems such as proteins.