A couple data points here from a lurker. I have an Ink Preferred as well as a United Biz card. Was applying for Southwest Performance Biz as it's time to re-up my companion pass.

I am a Sole Proprietor (have an EIN though) from freelance writing, 5k income, open for 3 years.

Applied last month and was denied for Business Structure. Called recon, no dice, still denied, they didn't like that I have a United Biz card that I got in January.

I went out and opened a Chase Biz Checking mostly because they had a $300 signup bonus and figured why not, opening it might help my chances. Reapplied (actually less than a month after the last application) and was denied again. Wasn't even going to bother with recon but did for the hell of it, went through the same business questions of which I have no fear because my biz is legit, and this time actually said I had been planning on closing the United card (also true). She asked if I would be willing to close in favor of getting the SWA card, which, absolutely yes. In the end she was able to do so and I was approved for the SWA Biz Performance card.

So -- I guess worth trying more than once. Hope this info helps someone out there!