Various people have reported this same thing — and it’s really not a problem – though you will find various opinions on the subject. Do some further research about h tags and SEO. It’s also not a simple task to recode a theme – which is what would be required.
I have no idea – having zero information about your site. But there are MANY factors that affect SEO and ranking. You would need to look at all the various factors and take into account that there is probably no single “reason” why your site is not ranking well.