And more, about the relationship thingun:
The couple´s relationship has grown stale.
A degree higher than fizzled out, I feel, because fizzled out conveys a certain "still there", the fire has just lost the spark, it was in the last throes, though. Whereas with "grown stale" it could be, but it could have finished (at least in the head of the one feeling it).
The couple´s relationship has lost the/that spark.