I feel your pain! We have had this problem with Chicklet, our Papillon, for the last year!!!! That's right, a year of getting up at 2:34 am to let her out. I have tried everything, and the only thing that seems to have slowed it down (not stopped, but I sure was thrilled to sleep through that first night) is to take her out by herself no earlier than 11:45 pm. I go out with her (we have a fenced yard so she usually goes by herself) and tell her to Potty outside like you would a puppy. After she goes, I wait and try to get her to go again. Staying up for the extra 45 minutes is definitely worth sleeping through the night. Good luck!