If your property value reduces and you refinance up to 80% of the reappraised value, your original mortgage amount may be higher than this amount. Thus, the new loan will not be sufficient enough to help you pay down the existing one.
Refinancing may not be that useful if you have already used up 90% or more of your home value in taking out a mortgage or any home equity loan. You won't be able to get the best rates available in the market as when you refinance a 90% LTV loan, you will probably require a loan of that value or higher. This will be quite closer to being a 100% financing option and hence mortgage refinance rates will be comparatively higher. Moreover, 100% loans are hardly available in times of mortgage market crisis.
Give yourself plenty of time to close. With most refinancings, your file is turned over to a closing or title company, which dictates the closing details. Like the lenders themselves, these firms are swamped when interest rates are low. Moreover, appraisers get backed up and can be difficult to schedule. So don't expect the closing to happen as quickly as anyone promises.
Once you know the reason for refinancing, you should ask your mortgage specialist whether or not it would be beneficial for you to refinance at this time or whether it may be more beneficial to wait.