Do you lose the counters on Azor's Elocutors if it's returned to your hand?
Yes, you lose the counters.

121.2. Counters on an object are not retained if that object moves from one zone to another. The counters are not “removed”; they simply cease to exist. See rule 400.7.
400.7. An object that moves from one zone to another becomes a new object with no memory of, or relation to, its previous existence.

So the Elocutors that’s in your hand has nothing to do with the one you previously had on the battlefield.
There is one card that overrides this rule: Skullbriar, the Walking Grave, but even that won’t keep counters in your hand. It really can’t, because the hand is a hidden zone. There would be no way of tracking which card it is that has the counters on it; keeping it separate from another card of the same name.