The entire process is set out in the Standing Orders.
If the subcommittee deems that an item is non-votable, the chair signs a report to be submitted to the clerk of the Standing Committee on Procedure and House Affairs as soon as possible. The bill's sponsor then has five days of meetings to appear before the procedure committee, if he so chooses.
That committee then decides whether or not to follow the subcommittee's recommendation, and submits a separate report on the item to the House.
The sponsor has two avenues of recourse: he may request a vote on the matter, but it must be supported by five other members representing a majority of the recognized parties in the House. Alternatively, he may inform the Speaker that he intends to replace the item with another item for which he has already given notice or will give notice in the coming days.