Homepage / Internal Page Rankings Swap

I have an e-commerce site and have noticed a strange phenomena. For my main keywords, my rankings remain fairly stable but the result that appears in the Google rankings frequently swaps between the homepage and the main category page. For many of my competitors, they will appear multiple times with multiple pages ranking for the same keyword. However, in my case, it is only one page or the other. Therefore, if it is the category page that is being displayed in the rankings, the homepage will completely disappear for the same term. Has anyone else experienced this? Is there any explanation for why this may occur?

You want to appear in search results when you search for a keyword (Nike shoes) for example, but you want it rank with more than a page from you website (home page and category page) for example.

If I understood correctly, simply you can't do that unless your website is really strong one and the competitive in this keyword not that high.

mahamad3 is pretty much right! You must be strong enough to list 1+ pages for the same keywords in search results.
I don't think you might have any problem with the on-site.

Branding SEO helps to list more n.o of pages.
Inner pages/category pages must receive more traffic to list for the same keyword. I mean just make the category page popular as like your Index page.

A little more info, D/A is 36, P/A is 48 for home page. Would that not be considered strong enough to rank multiple pages for the same keyword? And if not, is it normal for the pages to continuously swap in the search results? It seems to go back and forth every few weeks.