My players just hit level 13 and get to replace one old encounter attack power with a new level 13 power. Is there any reason why a half-elf player couldn't choose to replace his Dilettante power?
You cannot replace your Dilettante power with a class encounter power.
When you gain your level 13 encounter power, it can replace any of your class encounter powers. Your Dilettante power, despite being useable only once per encounter, is neither an encounter power nor a class power.
From PHB1, pg27, Powers (emphasis mine):
... At 13th, 17th, 23rd, and 27th levels, you can replace any encounter attack power you know from your class with a new one of your level (or an encounter attack power of a lower level, if you choose).
From PHB1, pg27, Half-Elves (emphasis mine):
Dilettante: At 1st level, you choose an at-will power from a class different from yours. You can use that power as an encounter power.
Your Dilettante power is neither an encounter attack power nor a power from your class, so it cannot be replaced by your level 13 power.