It is a bit complicated if we talk about SEO, and relate it to theme changing as the cause. But this problem is very common.
The main key point is in the way your site structure change (navigation menu, sidebars. layout etc). The more often you change your site structure, the more difficult for Google to recognize your site better. As an example, for some SEO reason Google “decides” to reward you Google sitelinks when someone type keywords related to your site (domain name, brand name, targeted keywords, and so on). When you change your site structure (ex: moving navigation menu from header to footer, changing theme that has significantly different site structure with the previous one), you may lose those sitelinks. This is one best example and reason why your site structure needs to be as consistent as possible.
Google needs time to recognize a site structure (onpage SEO aspects). Sometimes it takes months until Google finally decides that it knows your site well. If you often change your site structure, you will screw up the process. If you already have established recognition by Google (Good SERP rankings), and then decide to change your theme (that has very different structure with the one google has recognized), you will risk losing your rankings.
The best advice I can give is stick to your current theme and try to maintain it consistently. Or, if you have to change to a new theme, choose the one you think is better, and stick to it for a long period and try to maintain it from the scratch. In some discussions, I call this effort as “getting Google’s recognition back”.
Hope this can help. Sorry for my poor English.
Regards.