@Brian Breiding, I agree with @Jason D., don't give up because the first bank said no. When you say "the local bank", is this a bank you've worked with in the past? I doubt this is the only bank in town, if it is you might want to invest in a different town. But anyways, each bank will have their own requirements on properties they lend on, some won't lend on really small deals and some won't lend on bigger deals. Are your properties held in a LLC? If so, you will need a bank will offers portfolio loans that they hold internally, not all banks do that.
Personally, I am always looking for new local banks with more competitive terms or a bigger appetite for the asset I'm searching for. So don't give up, instead do the opposite, try harder. You have to remember, these banks are investing in you as well as the properties, so try walking into a bank or two or ten with a list of your holdings and show them why their investment would be safe with you.
Hope this helps,
Bruce