I hear from store managers all the time who want to become district managers, and they often ask how they can show recruiters that they're ready for the next step. It's not easy, and I remind them that they'll likely be competing against people who already have DM experience, which makes is that much more difficult. However, in order to give it your best shot, you need to demonstrate that you've achieved all you can as a store manager.
Here are some questions to ask yourself:
If you answered 'no' to all these questions, in all likelihood you're not quite ready for the DM level - not yet anyway. However, if you answered 'yes" to several of them, you may be, and that type of information may be valuable for you to communicate - on your resume, in your cover letter, and in interviews.
Of course it's possible that you answered 'yes' to all and you still don't get a chance (I can understand how frustrating that must be) but remember, recruiters want to minimize their risk, so they usually will prefer a candidate with multi-unit experience over someone without. But rest assured if you hang in there, continue to excel, and learn at every opportunity, your time will come.
I wish you all the best!