There is no such limit on the number of times you can go for home refinance loans. Most lenders prefer that you have no late payment for the past 12 months before you switch over to a new loan.
Homeowners who want to refinance but can't because they owe more on their home than their home is worth (also known as "upside down") should focus their time and energy on making more money. Adding a part-time job or starting a side business will bring extra income into the household, income that can be used to make extra payments a mortgage.
If your new mortgage rate seems too good to be true then it probably is. Check for hidden fees in your mortgage that will make up that suspicious difference.
Be Patient. Processing all of the paperwork that's required for a new loan takes time. Be patient while your loan moves through the system. Protect your credit score by paying your bills and making your mortgage payments on time and not taking on any more new debt than you absolutely have to.