Convergence sensitive to choice of baseline category?

Question

While running a simulation in R, I noticed that in fitting one particular model, R spits out a warning message, but if I simply change the baseline category in the response variable, it converges without complaining. The results produced do not differ appreciably, except that one value in the random effect correlation matrix is changed. I am curious why this occurs, and whether it suggests something interesting about the data set (the response variable is binary valued, and the explanatory variables are continuous-valued).

> library(lme4)
> fit1.MS.eE <- glmer(label ~ zSpec * zF1 + zF2 + (1 + zSpec + zF1 + zF2 | part), data = MSall.eE, family = binomial())
Warning message:
In mer_finalize(ans) : singular convergence (7)
> MSall.eE$label <- relevel(MSall.eE$label, "e")
> fit1.MS.eE <- glmer(label ~ zSpec * zF1 + zF2 + (1 + zSpec + zF1 + zF2 | part), data = MSall.eE, family = binomial())
>(no warning message)

I have uploaded the data set referred to in the code for interested persons.