It should indicate simply that the mean proportion of successes does not vary much across the 15 subjects in your study. The fact that the variance of the random intercept drop when you add your continuous predictors (the independent variables) might suggest for example that these are not fully balanced across subjects. If that is the case, the variability that was attributed to the random-effects (in the model with only the random intercept) is now explained by the fixed-effects (in the model with all the explanatory variables).
In principle having only 15 random-effects levels should not be a problem, even for maximum-likelihood procedures (e.g. package
lme4). However, if the variance of your random-effects is exactly zero, it is possible that your model is somehow overfitted, or that in your case 15 levels are too few (these nice simulations here illustrates the problem). If that is the case, check on this page, for example they suggest to use some informative prior on the random-effects variance.