In the skill description, it is said that you can only make one diplomacy roll per day to change a creature's attitude. The problem is that this change only lasts for 1d4 hours. As Wild Empathy is basically a Diplomacy for animals, it uses the same rules; so what if I want to befriend or tame a wild animal? I use Wild Empathy on him, play with him and after 1d4 hours he will just be unfriendly again?
You missed an important part of the Influence Attitude description, namely -
Any attitude shift caused through Diplomacy generally lasts for 1d4 hours but can last much longer or shorter depending upon the situation (GM discretion).
So, it probably depends on what you're trying to do. If you're just trying to convince an animal not to eat your or the party, the duration isn't really important...you make it work, the animal and your group go their separate ways. But if you let the GM know you're trying to permanently befriend the animal (like, as a replacement animal companion, or just as a trained pet), then he may or may not modify things to allow you to do so.
Remember, all this check is doing is modifying the animal's attitude. Training an animal is a totally different kettle of fish that even non-Rangers can do, so clearly Animal Empathy isn't required to do that. Handle Animal covers longer-term training.