The fire alarm panel in the office of the high school I work at one morning this week kept beeping for a battery trouble. The beeping would go away for some time at times and then come back. Even when someone would go silence it, it just came right back. One of the women in the office was so annoyed by it that she jokingly talked about putting a baseball bat to the panel.
Most panels resound active events like troubles & supervisories some time after they’re initially reported (& acknowledged) to help ensure they’re not forgotten about & eventually resolved.
This sounds like you’re maybe referring to an annunciator. This would require a key to operate, and for a trouble or supervisory there’s usually an ‘acknowledge’ (or ACK) button. Silence is usually designated for silencing the actual horn/strobes during an alarm.
The lack of a key for the annunciator is why the sound would turn back on instantly. If this is the case, you either need the key, or you need to find the main panel (often in a mechanical room in schools) to acknowledge there, which should quiet them both.
Acknowledging is fine, but the alarm company needs to come out to fix the problem, and as @TheCarson116 said, ‘Trouble Reminder’ is a thing, which will require the panel to start audibly sounding again every so often.