Writers talk about rejection all time – just part of job. But getting rejected by a no-pay publication really scrapes barrel. I know: it's happened to me more than once and now that it's been years [of therapy] later, I can admit lessons learned.
1. Competing Market
My first novice article submission was to an AboutCom site. The writing was good, and loaded with links to other helpful sites. It was latter that got piece booted. The website editor simply did not choose to publish articles that might lead readers to sites similar to her own.
This goes directly to "study back issues" mandate offered by experienced writers. Even if you don't agree with a specific editor's approach, you need to write to those specifics or submit elsewhere.
2. Preaching to Choir
Animal organizations are usually sorely in need of donations, whether financial, by way of goods or content for newsletters. However, an article on care and feeding of feral cats, garnered from years of experience in rescue work, was rejected on grounds that it was targeted to wrong readership.
Acting on that advice, I searched out and submitted to "how-to" publications directed at readers not involved in stray cat rescue, and published article multiple times. For example, a gardening ezine was interested in it from point of view of "pest control" rather than any humane reasons per se. Semantics aside, people who might never have read thing in some radical animal rights newsletter were potentially reached.