I worked for an alarm company, so I have to ask the basic questions:
Is this a smoke alarm, or a full on Alarm System (IE: Burglar Alarm, door sensors, key-panels, all that jazz). If it is a smoke alarm, Listen to those last few and replace the battery and/or alarm itself.
Now then, that out of the way, if it is a real alarm system (which I'm guessing by the fact you can reset it), usually the consumer's don't get a _real_ manual, so they can't just RTFM. My guess is one of the following is happening:
1) it was not only unplugged from the phone lines, but it itself was unplugged and is now running off of its quite ample internal back-up battery (they place car-battery size buggers in these things sometimes). Hence it will beep every so often until you reset it, then wait a bit longer before beeping again. Find the main panel, follow its cords and to find the power brick/plug and plug it back into the power mains (electrical outlet). It will start recharging and you can go on your merry way.
2) The other things are false leads, and there is a fault in an Alarm sensor, check to see what the key-panel or main panel LCDs are saying, and look for that zone. Fix sensor, or get company to. Run a reset once fixed, now no beeping.
3) It was set up to be a Monitored system (dialed an Alarm Company), and is now peeved it can't call home (the Alarm Company). It thinks there is a big issue. If you are still paying for alarm monitoring, then yes, you have an issue. Run a phone line to the little bugger. Even if you have IP-phone service (if you get phone through your cable, you do) it should still be able to do its low-baud modem tricks over that enough to call the company to do its status reports. If you are no longer contracted for Alarm monitoring, then pay the small sum for the company to come out and deactivate the bugger properly.
If you want advice further than that, I'll need more details.
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