SATTV:
https://www.vatnz.net/airspace/airport/NZHN says that Hamilton ATIS is 126.65 so make sure you are on channel.
If I recall you said you lived close to the airport so it might be that the front end of the scanner is overloaded when the tower hits the transmit button, the transmitter may not be in the tower itself, it may be out in a field else ware, this is rather common practice to separate the transmitter from the receiver to prevent overloading amongst other things.
John
Your source info for the ATIS frequency is wrong. 128.600 is the correct frequency.
The primary tower frequency is 122.900, 126.800 is used when it's busy as a second frequency.