Any experiences with medical alert buttons during power outages and storms?

Its been years since my Mom had one so hopefully they have improved. You needed a landline with hers. Don't thing a battery back up would work if the phone line goes out. Its probably electricity the backup is for. I have an answering machine landline phone that plugs in the phone with a cordless phone. When the electric goes out, so does the phone.

Our County Emergency management has a data base of names of people who may need help in emergencies. Because he is almost deaf, my husband is on that list.

There is a way to notify utilities and EMS that there is a vulnerable person living at that address.
In an emergency they will "try" to get to vulnerable people ASAP.
It is a good idea to have a generator,. Either one that is gas powered or a "whole house" one that will take care of everything. It will not get your phone service back, or the gas back but electric space heaters will help in the winter.
Asking EMS where your local Emergency Shelter is is a good plan so that you know where to go if you do need to evacuate.
Making sure that you have at least a weeks worth of medications and other necessary supplies is always a good idea.

If I recall correctly my mom's Phillips Lifeline system had battery back up, but I don't think it is realistic to expect any system to work in the event of large scale disasters. For those with no one near by to check on them our county had a system to register at risk individuals.