"Why my error handling function not working for multiple outputs?"
The problem has nothing to do with the two outputs, the problem is the inputs... namely that your function does not have any, even though the ARRAYFUN() documentation clearly states that "The first input argument of the error handler is a structure ... The remaining input arguments to the error handler are the input arguments for the call to func that made func throw the error." So it states very clearly, that inputs will be supplied to the function when it is called. The error handler example in the ARRAYFUN() documentation also show VARARGIN being used to collect all of those input arguments:
I already explained this and showed fully working examples in a comment to your earlier question:
For some reason you decided to ignore the documentation (and my examples) and remove the input arguments.
Result: errors.
Solution: accept the input arguments that the documentation specifies:
function [entryTime,exitTime] = entryExitTimeStampErrorHandler(varargin)
% ^^^^^^^^ You need this.
% why did you remove it?
PS: note that (also as explained in my previous answer) your error handler function could be reduced to this:
erf = @(varargin) deal(NaN);
