Sounds like you are hearing your battery back up unit. If that is the case, you will want to check the lights on it as it only beeps for 2 possible reasons. However since you say it has been beeping for 6 months, I will rule out it beeping because it is running on battery power.
Chances are the Replace Battery light is on, which means either your battery is dying and needs to be replaced, or the connection is just loose. I would suggest taking the cover off, removing the battery, and placing to battery back in to see if the light goes out on the unit.
If the light doesn't go out after doing that, and you have had the service for over a year, you can call 877-503-3537 for a replacement battery.
Fiber Solutions Center
Notice: Content posted by Verizon employees is meant to be informational and does not supercede or change the Verizon Forums User Guidelines or Terms or Service, or your Customer Agreement Terms and Conditions or Plan.