What are reasons for an error floor?

The algorithm is definitely working, but there is an error floor when I use higher-order statistics (specifically cumulants). The other algorithm I am comparing it to uses second-order statistics and does not have an error floor.

I am working on parametric estimation and I compute the root-mean squared error of the estimate, but the estimate floors out at some low RMSE. The floor is the same, regardless of the number of data samples.