You can refinance however you will receive higher interest rates. You can ask your lender for a forbearance agreement which will allow you to postpone or suspend payments so that you can catch up on mortgage payments.

You pay a late fee if your payment is more than 15 days late.
Your credit only reflects a late payment once the payment has gone 30 days past due or more.

The short answer is yes. Even being up to 120 days down you can still refinance. It comes down to equity.

There are specific lenders that can be matched to this type of situation. Typically called "sub-prime" lenders, they have a multitude of options available to you that can get you on track. Although the interest rates are somewhat higher depending on the lender and your specific situation, these loans are built to get you through until the mortgage lates drop off, allowing you to repair your credit and get back on track with a great loan and an excellent interest rate.

You can usually refinance no matter how good or bad your credit is, no matter how far behind you are on your mortgage. The type of financing though that you may qualify for with a poor mortgage history will probably be less than favorable. Along with a bad mortgage history come higher interest rates. The worse your mortgage history, the higher the interest rate you will be charged. If you do not qualify for a conforming loan or a sub-prime loan you may qualify for a hard money loan.

Lenders only look at the last 12 months of mortgage history. If you can wait the 12 months then the late payment will not affect your refinance in a negative way.

You can still refinance your mortgage but you will be limited to lower LTV's and may not qualify for low rate conforming mortgages offered by fannie mae or freddie mac.