Knowing the age of the panel its probably assumed that the bell is of a relative age. The advice given comes from the voice of experience, the panel over 20 years old, it has been on all that time, armed or not, it has been on, therefore its tired. If you left your tv on for 20 years would you expect the picture quality to be as good as new? Even well serviced alarm systems become unreliable as they get to the sort of age yours is, yours hasnt been serviced for several years by the sound of things.
The problem with alarm systems is they can be a nuisance when they start making noises in the middle of the night and the owner cant stop them, engineers dont like being woken up in the middle of the night to attend to alarm systems that have become a nuisance because the owner tried to save some cash, hence when you come here and ask we give the right advice. If its not what you want to hear thats not really our problem, we can only tell you what is right, because you wont thank us if we just told you what you want to hear, when the thing is going off at silly oclock in the morning and you cant stop it.