Depending on the value of your home, a drop of only $4000 over the last 2-3 years is pretty good! I have seen values drop about 20% during that same time frame in many areas of Saginaw.
So to answer your questions, I think it depends largely on the purpose of the Refinance, and how much more it would need to appraise for to avoid PMI. If you off by a few thousand, then it may be worth it. If you need to be 5% more, I don't think so.