Using parallel tempering, is it possible to swap too often?

In parallel tempering I have replicas of the Markov chain I'm studying evolving at different temperatures, and intermittently I swap the replicas on a nearest-neighbouring temperatures basis. Between swaps I evolve the replicas independently for $M$ Monte Carlo steps. Is it possible to set $M$ too small and stop the algorithm from reaching equilibrium? Or just cause it to perform worse than independent Markov chains?

The parallel tempering principle is valid for $M=1$, so one cannot switch " too often". When the swaps are balanced (as in Neal, 1999), the product of the powered targets is the stationary distribution of the multi-chain and the target of interest the stationary of the corresponding sub-chain. On the opposite if $M$ is large, swapping occurs very little and hence this sub-chain moves very little.