Why can't I refinance to lower my mortgage interest rate?

Our readers have sent in numerous questions asking why they can't refinance to a lower interest rate, which will make it more affordable for them to stay in their homes.

As interest rates reset, people in adjustable rate mortgages are finding their new rate jump to 7% or more. Meanwhile, mortgage rates for fixed rate loans are available at 5.5% to 6%, and with excellent credit scores possibly lower. So it's natural that these higher-rate people are looking to refinance.

Here's a recent reader question on the subject:

I have a 7% mortgage interest rate and wanted to refinance to a lower rate on my home.I got denied because they said my debt ratio is too high. I'm current on all bills. I keep 6k in savings for taxes insurance (not escrowed) each year. If you can pay the higher interest rate of 7%, why won't they give you a lower interest rate to lower your payments?

What's the answer?