That little coin cell battery has to last 7-10 years. To do that, your sensors broadcast a very short pulse, low power signal, and only when needed. Whenever the tires sit still for long, the sensors shut down and go to sleep.
Normal wake-up is done by an integral 2 axis accelerometer. Only after wheel rotation exceeds a certain speed will broadcasting begin. If too many signals are received in quick succession, some will be ignored, and the system will wait for the rejected signals to be broadcast again. Depending on firmware, that could take several more minutes. So yes, it can take several minutes to get a reading. If all signals aren’t received and logged in within around 20-30 minutes, the system should log a fault and show a blinking or solid light (depends on nature of fault).
If pressure is really low in the tire(s), the sensor should go into hyper-broadcast mode, and shout out a warning.