Residental Internet sold by Verizon is sold on the basis of a Dynamic IP. Whenever your connection drops, the IP is likely to change. Which is something to investigate - does your Internet drop regularly?
As an alternative, you should consider setting up a Dynamic DNS service to keep track of your IP address. That way, should it change, you can simply use a web address like "myhomeipaddress.dynamicdns.com" instead of your IP address, to access the camera. There are many free services, and some camera manfacturers often have their own service built-in to the camera which can be activated.