The owner, agent, or operator of any structure or premises shall have the right to appeal from any order of, or written notice issued by the Building Commissioner within thirty (30) days from the date such notice was given or mailed, or such order was issued, and to appear before the Board of Zoning Appeals, at a time and place fixed by the Board, to show cause why he should not comply with such notice. Such appeal must be in writing. Failure to file a written appeal with the Board within the time prescribed herein shall constitute a waiver of the right to appeal. Except in cases of emergency as set forth in Section 1409.05, filing of an appeal from any such notice shall suspend action on enforcement of such notice until the appeal is acted upon by the Board. No fee shall be required for an appeal made under this section.