Using line of credit on a rental property?
Most banks I've spoken with do not like loans less than $75k. Another issue you may have is seasoning. They may want you to hold it for 6-12 months. Check around with smaller local banks & credit unions.
Robert unfortunately the best answer you are going to get is "It depends". You should start with a local bank or credit union that would keep loans in-house. If you have a relationship with a local bank that is probably your best option. As @Chris Boundssaid, that's a small loan for most big banks and they wouldn't consider it. Best of luck.
You definitely need to try local banks and credit unions for a smaller loan like that. I think it will be easier finding a place that will loan the amount you are requesting than it will be to find a bank that has no seasoning requirement. If you find a bank with no seasoning, feel free to share with others.
My experience has been that some local banks or credit unions could do what you're looking to do. You have to talk to the right guy, not everybody at a bank is going to know what a "portfolio loan" is, and you'll most likely be talking to the commercial loan originator. I've seen many options, like encumbering one property to buy another, and offering lines of credit on something like the $25k house you have there.
I have a heloc on a rental property that I never occupied. I went to a large, regional bank that is owned by, or at least heavily invested in by Wal Mart and they gave me a 5 year, 3.99% fixed rate heloc during a spring promotion of their's a few years back. And yes, they knew from the on set that this was a rental property. But it was still funded by a regular mortgage person on the consumer side of the bank. They sell their 1st mortgage positions on the open market but keep helocs and home equity loans on their books. That's how most banks do it. Helocs and Home Equity loans are way cheaper in terms of origination costs compared to traditional mortgages.
I take all rental revenue and apply it to the heloc until it is paid off and advance the heloc for all repairs, tax payments, insurance expense etc. I have even used it to cover down payments for other purchases. In fact, I am advancing it to cover my 20% down on a duplex I am buying.
There are places that will do it. You will just need to find one that will in your area.