When the person answers the call and presses any button on the keypad, the alarm keeps dialling, the message keeps repeating and moves on to the next number?

This is not generally due to a fault with the alarm. If the alarm keeps playing the recorded message, and moves on to the next number, it means that it has not received the ‘beep’ that is generated when the recipient presses any button on their telephone keypad. It is getting blocked in the phone system, once it has made its way to the alarm user’s house. You can try 3 things here:
1) Press and hold the number on the keypad for 2/3 seconds to create a ‘long’ beep
2) Make sure that the alarm is plugged into the main telephone point in the house
3) Try it in other telephone points in the house