I crack up at questions like this because the answer is inherently in the question. No. You do not need to keep beating a dead horse. To use your metaphor, if you're trying to get something from the dead horse (like you're trying to get something from the contacts you have) "beating it" will not help you achieve your results.
So, let's address the matter at hand. You have contacts. You want something from your contacts that you aren't getting. Here are some of your choices:
1. Start over. Get new contacts.
2. Re-evaluate what you're asking for. Are you giving your contacts something they can say YES to? Many times you may think you are, but if you're continually getting no (and no response is a no), then obviously you're not.
3. Try a new approach. Help your contacts instead of seeking help from them. Be a connector for them. Seek out leads for them.
4. Get involved in social activities with contacts so you know you're connecting with like-minded people. Sometimes the contacts we have are not necessarily the contacts that are "right for us." Building business relationships in a creative industry is more like dating than many of us care to admit.
So lay the horse(s) to rest. No more beatings. It's not good for them, it's not good for you.