I'm not familiar with AppHarbor's setup. But if it's using IIS, the pinging is just keeping the application pool from reaching the idle timeout. But there the default IIS setting for the application pool to be recycled every 29 hours no matter the number of requests. And it's normally in the best interest to let it recycle once in a while, so working around it may not be in your best interest.
Your best bet is to reduce the number of things happening on application start. Precompiling your views is a good place to start. And heck, Stack Exchange/Stack Overflow precompiles views to avoid the application start up cost.