You could choose to have another appraisal, but you will have to pay for it again. The chances of it coming in high enough for you to avoid PMI are slim. If you would like to see home values in your neighborhood, go to www.SaginawHomeValues.com and enter a little information about your home and it will show you all sales activity near your home. This of course is a general value.
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.