If this is wrong, I shall be very confused.

the walk always seems longer - Highbridge is deceptively long
when time is a factor - Auron has to run to catch up to the others
with a friend's life on the line - Kimahri attacking Seymour on his own
after the death of another close friend - Maester Kinoc

The answer is the second battle with Seymour at the Highbridge, and seems to relate directly to Auron, who is the only person to consider both Kimahri and Kinoc a friend.