Why didn't the surviving men in the Battle of Thermopylae retreat rather than face certain death?

Of course, we can't know the answer to this in any certain
way because the men did not leave notes explaining
themselves.

Perhaps the most likely explanation is that the
men were both patriots and dedicated soldiers.  This means that they cared a great deal
about their home "countries" and about their fellow soldiers.  Both of these would be
reasons for staying and fighting so that the rest of the Greek armies could get away and
regroup instead of getting slaughtered as they
retreated.

It may be also that the men were willing to die
because of the heroic tradition in Greece.  These were men who would have been raised on
the stories of the Trojan War and who would have taken seriously the idea that the gods
favored those who were valiant.  This might have been another reason to stay and
fight.

Again, we simply can never know for
sure.