Article 164 specifies when a tax postponement expires. The deferral of payment ceases to be effective—and the tax becomes immediately due—upon two events: (1) the date specified in the new assessment issued after the objection decision, or (2) the date the taxpayer abandons the dispute. This ensures that the postponement is strictly temporary and is only valid as long as the dispute is active. Once a decision is made or the objection is withdrawn, the taxpayer must settle the outstanding balance according to the Authority's final determination.