Why would Peter NOT have a successor?

According to chapter 1 of Acts, Peter argued for a successor for Judas, stating, "For it is written in the book of Psalms, `Let his habitation become desolate, and let there be no one to live in it'; and `His office let another take'" (Acts 1:20; RSV), and Matthias became that successor. Why would another not take Peter's office after his passing?