If you want to succeed as a writer, you must be persistent. Make a list of potential markets for each of your articles. If your manuscript is rejected by choice number one, check for suitability, make any corrections and mail to choice number two. Keep accurate records of where your story goes and learn from your rejections. List the magazine, the date your manuscript was sent, and the date you received a response. In this way, you'll avoid the mistake of resending the same story to the same editor.
Any time an editor takes the time to write a personal note with suggestions for improvement, make those corrections. Several of my own sales have been a direct result of rejections which were returned with ideas for changes. By following the advice, I turned flawed manuscripts into salable ones.
Sometimes, if you can't sell an article in its original format, you may need to adjust the way you are presenting it. One idea I tried to market couldn't find a home, although I knew the information was valuable. The original article was a third place winner in a national contest, yet wasn't marketable as written. After a number of rejections, I hit upon a new way to present the material and sold not one, but two articles to the same magazine on the original subject.
Have faith in your work and never give up. I've found over the years, it is often a case of being in the right place, at the right time, with the right material. What one editor could care less about, another may snap up in an instant.