Where the use or erection and construction of the principal building or structure for the construction or use of which a variance or special permission has been granted by the Board of Appeals shall not have been commenced within the original one-hundred-twenty-day period by reason of weather conditions, circumstances beyond the control of the applicant or otherwise, said Board may, in its discretion and without public hearing, grant one or two extensions, each of 60 days or less, where the applicant shall submit proof in writing of all the facts and circumstances and such other proof and material as said Board may require; provided, however, that the conditions upon which the variance or special permission was granted originally have not changed substantially or materially in the judgment of the Board.