Answer

Yes, an Acolyte with the Genesis or Last Word attribute can activate those abilities multiple times, but only under specific circumstances:

• Genesis: This attribute is resolved when the Acolyte is deployed onto the battlefield. If an Acolyte leaves the battlefield and is later re-deployed (for example, by being destroyed and then returned from the Discard Pile), its Genesis ability will trigger again upon its new deployment.
• Last Word: This attribute is resolved when the Acolyte is destroyed. If the Acolyte is destroyed multiple times (i.e., it leaves and re-enters the battlefield and is destroyed again), its Last Word ability will trigger each time it is destroyed.

This is supported by the following rulebook references:

• Page 15 (Section 4.4 - Replacing):
  "If the destroyed Unit has the Last Word attribute, you must resolve it before the new Unit enters into the battlefield. The Unit that enters into the battlefield is actually deployed, thus it is exhausted and its Genesis attribute must be resolved (if any)."
• Page 19:
  "Effects of some rituals may activate some Last Word attribute. In that case, Last Word is resolved after the Ritual is put in the Discard Pile."

This means:

• Each time an Acolyte is deployed, its Genesis triggers.
• Each time it is destroyed, its Last Word triggers.

There is no rule in the provided context that limits these abilities to only once per game or per card.

Source: Page 15, Page 19

Source: Core Rulebook (pp. 15, 18, 19, 22, 8)