
If I'm not mistaken, this is the usual sort of precaution against loss of
communications.  That timer is counting down continuously; if it ever hits
zero, that means Galileo hasn't heard from Earth in a suspiciously long
time and it may be Galileo's fault... so it's time to go into a fallback
mode that minimizes chances of spacecraft damage and maximizes chances
of restoring contact.  I don't know exactly what-all Galileo does in such
a situation, but a common example is to switch receivers, on the theory
that maybe the one you're listening with has died.