It's not uncommon for polar flights to lose GPS signal (ionosphere issues due to the high latitudes). But it is not a concern because the typical IRS drift is 650 meters for every hour of flight, and the skies are empty (compared to the Atlantic tracks) in those regions.
Sooner or later GPS will be back, navaids will be within reach, and radar coverage will resume.
Q: Now, what happens when the GPS signal is lost? Does the FMS navigation start to drift from this point on, or does it switch to all the accumulated IRS drifting that's been going on for hours prior?
One way to picture the latter (I guess), is the magenta line on the navigation display to abruptly shift away from the plane-symbol, even if it is just by a mere few nautical miles.
My question applies to the older IRS systems that require stationary alignment, unlike the new GPS-coupled align-in-motion systems found on the 787, etc.