NavList:

"There is an additional event which recently came to mind.  A coronal mass ejection, commonly known as a solar storm, can take out satellites.  I wonder about the vulnerability of the GNSS system to this type of event.  If you have the time, Dr. Langley, I would appreciate it if you could educate us! Thanks!"

This article discusses the effects of solar activity on GPS (and, by inference, other GNSS) signals: http://gpsworld.com/innovation-gnss-and-ionosphere-11036/

Reduced signal availabilty and accuracy are potential outcomes. If by "can take out satellites" you mean damaging the satellites themselves by corpuscular radiation as has happened to some geostationary communication satellites, you should know that GPS satellites are hardened against radiation so the likelihood of them being damaged by a solar outburst is low. The GPS III-F satellites will have even more hardening, not just to protect them from solar outbursts, but also to protect them during a possible space war: https://nationalinterest.org/blog/the-buzz/air-force-hardens-satellites-prepare-space-war-think-russia-25027

-- Richard Langley