For a relationship to endure through the ages successfully, 2
critical criteria must exist :
1. Love (feelings)
2. Commitment (mental dedication, devotion)
Feelings can rise and fall, come and go. If they are there all
the while, staying in a relationship is all the easier. But this is
idealistic because under harsh circumstances like stress,
lovey-dovey feelings can be rxtremely scarce and indeed hard to
come by.
It is in hard times like these that even despite a couple run on
empty in the passion/emotion department that the mental faculty
should take over to persevere with the relationship for its
sake.
A successful relationship should be like a bouncing ball. When
it falls, it must bounce back up so that a game can be continued to
be played. If it falls and goes splat on the ground, it's no use at
all.........
So in the final analysis, it all depends on what kind of
relationship TS is referring to.
For a fling, yes, it's time to go when the passion runs dry.
However, if it be a steady relationship, passion running dry
should never be the reason to end the relationship. 
