You can use the more spore multiple times, as long as this doesn't result in more than ONE pokemon in the enemy team sleeping because of some move you used.
Example:
1. You use spore first time, 2 turns after the enemy pokemon wake up. You can use spore again.
2. You use spore first time, opponent switches pokemon while the other one still alseep because of your attack. You can't use spore again.
3. Your opponent uses rest and one of his pokemon is asleep. He switches, you can use spore on that pokemon, because the sleep status was "self-inflicted".
Hopefully this clears your doubts