Channy, the MGL states 40 or 45 days, but there are NO teeth to that law. There is no penalty for the PD that drags their feet and holds out for 6 months or even a year. [I know someone who was dragged thru 4 PD interviews and 6 months prior to their issuing him his LTC-A/ALP and that was a recent renewal (NOT a 1st time issue)!]
You might talk to them and explain your problem, but if they don't like issuing LTCs, they can do what they want to with no fear of repercussions (from a practical viewpoint). [Legally you can sue them after the time limit of 40 or 45 days, but you are unlikely to win in court.]
In MA, all LTCs are "discretionary" which means each of 351 towns/cities can do what they like, require what they want, discriminate at will (except against protected classes of people).
Good luck!