We are both in the real estate profession and own a few properties we have posed this exact question to. We base our decision on:
Will we own the property longer than 10 years? If not, we don't feel the savings versus the closing costs outweigh the process. If you are planning on staying in the home, than yes, the savings will be worth it.
Can we afford the monthly payments and how drastically will they change our payment? If it will save us less than $100/month, for us, that is not worth it as at any time plans can change and we would have to sell earlier than later.
With a recent purchase and with the stricter guidelines for refinancing and the current market values stable or declining, would we really qualify for the best rate if we don't have 10-20% equity in the property?
Are closing costs going to run 2%? Adding the closing costs into the loan will add to the payment, not improve it and do we want to pay the cash out of pocket?
It's an individual decision. If we had 15-20% equity in a property and were planning on holding on to it for at least 8 years, we would most likely re-finance as long as closing costs were at a minimum. We would go to who currently holds our mortgage first as that is the best best to have the lowest closing costs.