You hit the Pending Authorizations limit when you have many authorizations still pending at the time you try to create new ones. You probably have many authorizations pending because you're creating many New Orders, and then not fulfilling the challenges for those orders. This might be because you've written your client to place many orders in parallel, or it might because your client is failing somewhere along the way and leaving old orders behind.
You can fix this in two ways:
make sure your client actually attempts to fulfill every authorization/challenge it creates, and doesn't leave them hanging around.
make your client delete old pending authorizations by deactivating them. Not all clients have the ability to do this built in, but it is supported by some.