Is it just your home Wi-Fi network that's affected?
Hate to start an response with a question, but yours is kind of the opposite problem from the ones I've been hearing. I've been hearing of Wi-Fi turning its self on after being in airplane mode, or over prompting for the user to try and connect, or connect to an available network.
Anyway, if it's just your Wi-Fi that's affected I would say it's one of two things.
-Security protocols or something else has changed either on the phone or your network OR
-Your network needs to be rebooted.
Since, for me, the latter would be easier that would be where I would start. Unplug both your router and modem. Wait 15 to 30 seconds and plug in the modem first then the router. When you have all of the lights on each try your connection again. I've found that, again for me, I may not lose connectivity for my wired stuff, but may loose Wi-Fi.
If you think it's the former, I'd try telling the phone to forget your network then setting it up again. If that doesn't get it you could try changing your security protocol for your router. Afterwards you'll probably have to redo your setup on the phone anyway.
If neither of these works, tell us what Verizon had you do, so we're not rehashing the same things.