Sure, gps geek and time-nut here.

The rollover problem is a hard one to fix, because there's no reasonable way for a GPS (at least one using LNAV (legacy) signals -- pretty much all of them, though I don't know what modern passenger jets use) to know which GPS "epoch" they're in. If you don't know what epoch you're in, you don't know what the date is.

Some GPSs solve this by recording the week number of their firmware build, and if the signals they get indicate the week number is less than that, they assume they're in the next epoch and update accordingly. Still means you run out of time, but you get a full ~19 years of life first (and then fail at some random GPS week). Some use fuses to record when an epoch has passed. Some use out of band information. Some store the current epoch in flash or battery-backed RAM. Some just never address the problem.

Thing is, though -- the only effect this has, is that it makes the GPS return the wrong date. That's it. The week rollover has no effect on navigation unless there's some significant bugs in the unit, or something external to the GPS relies on the date being output and doesn't deal well with the date suddenly going back in time. That's it.

I'd be kinda shocked if airplanes were just jam-syncing the clocks of their nav computers to the output of a GPS, and then had those nav systems be dependent on that time. But then again, I work in the tech industry, and I've seen the kinda code that goes into most products, so maybe I wouldn't be that shocked.

(I also can't imagine that GPS units used in aircraft aren't directly tested for their behavior during the week rollover. It's a well known and understood problem, and even if some random GPS manufacturer drops the ball, stuff that goes into aircraft has to go through certification for a reason...)