Gas Pilots going out
A healthy home pulls in air, circulates it, and releases it. You have negative pressure when you are releasing more air than you are pulling in. This could be caused by a blocked intake or an over-working exhaust system. The most common, for a stove, would be a vent hood pulling too much air from your home than it can pull in to keep the fire going (see figure 1 above.) However, since this is happening throughout the house, it could be multiple fans that are leading to the overall problem. The best way to test this, no joke, is to open a window near one of the fires and see if it can stay lit then. If it can, then it is negative air pressure within the home. If it goes out, you might be having issues with your gas line.. possibly a partially closed valve somewhere or issues further down with your meter even.

This is most common with wood fires as they draw a lot of air to keep going, but it's the same concept for any fire. Try opening a window and see where that gets you.

As for fixing negative pressure.. that comes down to the systems in your home. Either you're not getting enough air coming into the home, or your house is pulling too much out. Have you had any changes to your HVAC system?