The matchmaker comes at ages 5 through 9. It is very rare for the matchmaker to come at age 5. After that, she will no longer visit you. She comes at 10:30 AM, 3:00 PM, and 7:00 PM.
If you keep refusing the matchmaker, it will turn into an oldie. When it is an oldie, the matchmaker won't visit you anymore. You will need another tama of the opposite gender, that is a oldie and mate them. Their babies will quickly change into the secret character, Oyajitchi.
You can always set the time to 6:59 PM and wait one minute, and she will come. *Sometimes this does not work, however.*