python 3.3 : scipy.optimize.curve_fit doesn't update the value of point
It is normal for the objective function to be called initially with very small (roughly 1e-8) changes in parameter values in order to calculate the partial derivatives to decide which way to go in parameter space.  If the result of the objective function does not change at all (not even at 1e-8 level) the fit will give up: changing the parameter values did not change the result.  
I would first look into whether the result of your objective function is really sensitive to the parameters. If the changes to your result really are not sensitive to a 1e-8 change, but would be sensitive to a larger change, you may want to increase the value of epsfcn passed to scipy.optimize.leastsq.
I am trying to fit a custom function to some data points using curve_fit. I have tried 1 or two free parameters. I have used it other times. Now I am struggling to make a fit, because the algorithm returns always the initial input values, with infinite sigma, no matter what the initial values are. I have also tried to print the internal parameters with which my custom function is called, and I don't understand, my custom function is called just 4 times, the first three with always the same parameters and the last with a relative change of the parameter of 10^-8. this doesn't look right