The OP's question is easy to answer. I have 7500 alarms installed in the field and I'd say 50 of them are operated by people who realise a bit of maintenance is needed
There are 2 basic problems
PIR detectors are sensitive to supply voltages
Some makes like Optex have a delay while the device powers up
Then some people will have a normally closed radio receiver for remote panic
In a Paradox panel, the bus will shut down when the panel voltage reached 10.2VDC. If the battery is dodgy, this can occur within minutes. A good 8 a/h or 9 a/h battery can easily manage 10 hours reserve time
The alarm panel also has "watchdog" circuitry. This will ensure that should the power fail and come back on, if the alarm, were already armed, it will power back up armed
A radio transmitter aerial, even a 25 watt transmitter should not affect an alarm panel, provided it it in a closed metal box. A plastic box is no good. Substantial RF rejection is built into the panel.
Early (pre 2004) IDS 400 and 800 panels appeared to suffer from this type of interference. Some would even trigger if a flourescent light was switched on in the same room
A PIR might power back on normally open
A radio receiver can "chatter" if the supply voltage is unstable (a flat battery pulling down the bus voltage