TL;DR -your DA is small because your business is small. Period.
Domain authority is just a number. PR is also number.
You can rank very well also with little DA, same is with PR. Focusing with DA improvements is meaningless because DA can become higher with links/linkbuilding. And links can be earned with good content or forced with SEO linkbuilders. This definitely can improve little bit your DA. Even in SEO there is term "PR sculpting".
Playing with DA and site is same as "which came first, the chicken or the egg?". If your site grows with links then DA will be increased. But growing from 40 to 50 is same as growing from 0 to 40 as links. And from 50 -> 60 is same as 0 to 50. All happening due their logarithmic scale for parameters. And this require huge works.
So let's go back on "chicken/egg" problem - you can improve DA if you get links from trusted newspapers with sites as Guardian, Independent, Mirror, Daily Express, Telegraph, etc. Also can be trusted magazines with sites - Glamour, Elle, Wired, etc. You can get links from TVs - BBC, ITV, C4, C5, etc. You can get links sponsoring events - like BigBrother, X-Factor, etc. Then your DA will become higher. Now let's face question again - you're small and to make that media to talk about you need to grow to national wide and become giant in your niche.
And how you grow is different story that we can't answer without market research, financial analysis and some forecasts.