Since you had the problem before you switched service, I have to assume the source of the problem is with your phone system/devices. How many and what type devices do you have? Phones, ringers, fax machines, flashing lights, etc... Try removing them one at a time and see if the problem disappears. Also check for any surge suppressors on the line that may be shorted or leaky.
..
A phone service has to be able to detect the difference between the on-hook and off-hook condition in order to connect or disconnect the line. If it can't, then the system does not operate properly, either hangs up prematurely of won't hang up at all. It detects the condition by sensing the current drain or load on the line; too heavy a drain or too light a drain and the system reads the incorrect condition. The drain normally increases when you lift the receiver (off-hook) or decreases when you hang up (on-hook). My guess would be that you have too heavy a drain. Each device has a label that indicates it's individual drain or REN (ringer equivalency number). This is based on a value of 1 for a typical old-fashioned ringer phone. Digital phones usually have a number less than 0.3. The phone system can support a total amount that depends on the design, usually from 3 to 10 total. You can see that there was once a fairly low limit of how many extensions you could have.
..
As for the "cod", I guess that the tech had a way of adjusting your standard drain threshold to accomodate your system. That may or may not be true for fios. You should ask yourself why your system needs a special setup to function properly and address that at the source (your devices).
About a year ago when I had the old phone (POTS) service. I had the opposite problem with the line going on-hook. That turned out to be a defective device in the phone company's switch panel down the street. With fios, I doubt that Verizon uses the same switching technique or hardware, but I am not sure.
If you are technically inclined and have a voltmeter/multimeter, you can test the line drain yourself. It should read about 48 Volts DC when all phones are on-hook and should drop to under 12 Volts DC when a phone is off-hook. Do not touch the line, it can surge to 100 vac when the line "rings". It is low current, but nevertheless can give you a very uncomfortable shock.
