You don't say how the rental property is currently mortgaged or how much the property is worth. If you bought the property between 2000 and 2005 in an area where the housing market was very hot, you might have trouble getting refinancing for any or all of the following reasons:

1) Your home has lost a significant amount of value. I put a small house on the market in 2006 moved to a different state to take a job in 2007. By 2008 that house lost 75% of its value and was so badly upside down I could not give it away, The bank finally took it back, hallelujah--but not everyone in that rustbelt city was so lucky. That same bank 'dumped' hundreds of rental properties on the city by foreclosing, kicking out the homeowners or tenants, then never selling the properties at sheriff's auction, which in that state legally left the home titled in the original owner's name--the person who thought it had been repo-ed--and the problems with the city, who got the calls when the homes were gutted and vandalized. Not that it will be THAT bad for you--I'm just sayin'. It's ugly out there. Nearly one-third of all mortgages are upside down right now, and not just subprime or recent mortgages--all mortgages. Trillions of $$$ of value was lost after the crash.

2) The refi won't cover the balance left on your existing mortgage. The best you will be able to do is an 80% refi and depending on your credit and where the house is located and what it is currently worth you may have trouble getting even that. So do the math and see if a refi will really help you.

3) Your property is worth too little. Most mortgage companies and banks don't want to touch anything worth less than $100,000. In some parts of the U.S. this doesn't apply to ANY homes. In other parts it applies to most of them.

4) Your property is worth too much. Jumbo loans are capped at around $417,000 right now in most parts of the U.S. or 729,750 in very high cost areas. The practice of cobbling together a HELOC (home equity loan) with a jumbo mortgage to cover the cost of financing has been pretty much discontinued, as have most other 'creative' financing practices common during the boom.

5) The fees make refinancing cost-prohibitive. You will pay loan fees on a refi and they can be substantial. The national average is 3% of assessed value but in some parts of the U.S. that amount is as high as 6% and for some lenders it can go much higher. Broker fees can be well hidden in the terms of a mortgage, so it pays to have an attorney look the papers over before you sign. Federal laws require lenders to disclose fees on a rigidly defined schedule in very specific ways, but lenders don't always comply. (See links below--Citi was fined $1.25 million for noncompliance.) Lenders can be shut down if they don't comply, but they count on you not knowing that and most people don't know it.

6) Your credit isn't perfect. It will need to be near-perfect to get financing right now--over 700 at least, and over 720 is better. Banks still aren't lending like they were, despite all the great press about how the economy is turning around, and they're being very, very careful about who they lend to and what they lend against.

That's the bad news. But even if all of that looks like trouble for you personally (and hopefully none of it does), you aren't without recourse. If refinancing doesn't work out and you are paying too much interest or are having trouble making your mortgage payments for any other reason, you can still attempt to negotiate a loan modification with your original lender. How to do that is kind of a separate question but in general, it helps to work out the terms in detail ahead of time as opposed to approaching the lender and saying, "I want a loan modification," without any preparation.

Again, the fact that it is a rental property will make the bank less likely to consider a loan modification for you--on the other hand, some banks are showing signs of saturation when it comes to foreclosure and seem a BIT more willing to negotiate than they were in 2009.

Finally, if at all possible, consider simply increasing the amount you pay toward the principle each month. In effect that's a free refi. No fees, no added costs, and you pay off your loan much more quickly. Bankrate.com has a slew of calculators that will tell you how fast you can pay something off making additional payments to the principle. For many people that option makes a lot more sense than refinancing.