It sounds like something is wired incorrectly in your home. The Rogers Modem should be properly connected to the "wiring block" of all your phone lines in your home and all the phones in your home should work properly when connected to the various home phone jacks throughout your home.
It is not necessary, for example, to have a cordless phone base connected directly to the modem. I have all kinds of corded phones (and cordless phone bases) connected to various phone jacks around the home (as they were with Bell POTS) and they all work fine.
One year later update since this was only fixed just now as the security system started making noise as the old phone line had finally become inactive since switching home phone to Rogers a year ago. Called security company who said to call Rogers. Called Rogers and they booked an installer that never arrived. Called again days after and got it rescheduled. The installer came and unplugged the modem from the cordless base and moved it to the basement and installed it properly allowing all phone jacks to start working properly and reconnecting the security system. Told us the previous installer did it incorrectly. A lot of hassle but finally fixed.
Ignite works for television and internet but has too many issues for the home phone. Whenever the phone rings the phones clock goes ahead by 15 minutes ( Rogers says that it is working on this problem, which is effecting many customers ). Second thing, sometimes calls do not come through. The Rogers technician blamed my telephone and had me replace all my home phones. The problem still persists with my new phones. Now Rogers is sending out a senior technician to take a look at this problem.
My Internet and Phone was down for a few minutes around 11:05AM on Friday, but it was back up in about 5-10 minutes. Other people have also reported similar sporadic outages, but not something lasting as long as yours...