Thats because their INS (Inertial Navigation System) has already
been GPS aligned. The GPS component is just there to tell the bomb
where it is at that point of time. You don't really need the GPS to
be up to have the bomb hit the target, cos almost every coordinate
is already GPS mapped already.
Hence, there is INS component of a GPS/INS system. The GPS just
needs to be there to align the aircraft's location before the
mission launch, and the INS basically does the rest of updating the
JDAM.
From what I understand the GPS updates are not instantaneous, and
there is a certain amount of lead time. Hence, for a missile or
bomb weapon, its "updated" coordinate would be lagged, if not for
the INS component as well.
But say in a prolong conflict, where the GPS is taken out for
almost a month already. A lot of INS onboard ships, and aircraft
would be misaligned. Now that would affect the accuracy of
JDAMs.