Sounds like your Verizon modem may be having a connection problem. We had a similar issue with Comcast and found out they upgraded in my area and had to send a signal to my modem. I would insist they send you a new modem especially if you are renting it or bought it. Sometimes they outdate and no one tells us. If it's a phone line problem they should be checking that too. I don't think your mac has anything to do with it.