here's the deal, if you are going to be paying a lot just for a security system, you should not have it hooked up to any form of VOIP as it doesnt take much for it to go down. KeepOnTruckin is correct in that POTS does not go down unless the connection is physically severed as it supplies it's own power. however, FIOS is much better than Cox internet service and i would only suggest you switch out the VOIP for a POTS connection. you could be in the same situation if you had cox and your cable modem died.
"the wisdom of the wise will perish, the intelligence of the intelligent will vanish."