At any time and from time to time, after completion of the original construction of any such district's system of improvements or after the completion of any alteration, reduction, enlargement, addition to, or other improvement of the system not constituting maintenance, as herein defined, the board may upon their own initiative, or upon petition filed by at least ten percent of the total number of owners of property within the district subject to assessments for maintenance, as shown by the latest assessment roll of the district shall, fix a date for and hold a hearing at the county seat for the purpose of determining or redetermining the special benefits accruing from the maintenance of the district's system of improvements to all property benefited thereby.