Thanks for the question Jim, and it's a good one. Down payments are one of the most misunderstood parts of rental property investing.
The general idea is that down payment and potential return have an inverse relationship. In other words, if you put 20% down on a rental property, there's typically an expectation that you'll get a superior cash-on-cash return than you would if you put 30% down.
On the other hand, there's the question of cash flow. The "superior returns" I just mentioned include equity appreciation plus cash flow, but as you correctly point out, there's usually a minimum down payment amount where a given investment property will produce positive cash flow. After all, the lower your down payment, the more money you'll have to borrow, and the larger your monthly mortgage payments will be.
And every rental property investment is different. The down payment you need to produce positive cash flow depends on several factors, including the particular market you're buying in, terms (such as the interest rate) of your mortgage loan, and the nature of the particular real estate deal itself. In other words, there's no one-size-fits-all down payment that will guarantee you positive, or adequate, cash flow.
It's also worth noting that regardless of cash flow, lenders tend to require significantly higher down payments for investment properties as opposed to primary residences. For example, Fannie Mae's (OTCMKTS: FNMA) lending guidelines require a minimum of 15% down for a single-family investment property and 25% down for properties with two to four units. Even if you can qualify for second-home financing for a property you're planning to occupy some of the time and rent out when you're not using it, you'll need a bare minimum of 10% down. Asset-based lenders require at least 20% down for rental property loans -- and that's assuming the property generates enough income to justify a loan with such a small down payment.
In fact, other than using a house-hacking strategy with an FHA mortgage, where you live in one unit of a multi-unit property and rent out the other(s), there aren't many options to put less than 15% down for any long-term rental property.