Unless your structure is incorrectly wired (like a lot of those circuits being tied together somewhere), the only thing in common to the failing GFCIs is the power feed.
I would start by a) shutting off the main breaker, and b) opening the main breaker panel and inspecting the main leads, especially the neutral/ground from the meter. Give them a firm tug and make sure they are extremely secure. Be sure to stay clear of the wires from the meter to the main breaker: They are live! Even though the main breaker is off.
Also, examine the neutral bus connection(s) to the ground/neutral terminal strips: In every Square D panel I have seen, there are bolts which connect the bus bars together. Other brands may use a heavy wire with each end in an eye nut arrangement which goes over a bolt into the bus bars.
Especially, if there was recent wiring work, check that all those circuits have their neutrals properly run to the breaker, the "curly white wire" secure in the ground bus, and all the grounds securely in the ground bus.
Next check that the ground rod is intact and the wire which goes into the service panel is securely connected at both ends. If there is any doubt, go ahead and remove it for a few minutes to polish the copper wire and rod into the clamp with 100–400 grit sandpaper, wire brush, steel wool, etc.
Next, look at the meter and service wires (if above ground). Are they in good shape?
If all of those are beyond question, call the power company. They will probably repeat the latter steps, but will eventually escalate it to a electric technician which will come armed with a meter to see what is going on. They probably have a faulty neutral or bad ground on their side.