I think it is natural for h2 tags to be titles of the paragraphs. If you have few paragraphs on the same page it is a natural to have title (h2) for each paragraph.

....................................................
<h1>Title of the page</h1>

The page introduction text.
The page introduction text

<h2>Title of the paragraph</h2>
The paragraph introduction text.
The paragraph introduction text.

<h3>Title of the sub-paragraph</h3>
The sub-paragraph text.
The sub-paragraph text.
The sub-paragraph text.

<h3>Title of the sub-paragraph</h3>
The sub-paragraph text.
The sub-paragraph text.
The sub-paragraph text.

<h2>Title of the paragraph</h2>
The paragraph introduction text.
The paragraph introduction text.

<h3>Title of the sub-paragraph</h3>
The sub-paragraph text.
The sub-paragraph text.
The sub-paragraph text.

<h3>Title of the sub-paragraph</h3>
The sub-paragraph text.
The sub-paragraph text.
The sub-paragraph text.
......................................
I use above structure for long articles because is good for reader experience. I have never been panelized for it but I am wondering what other members think about this issue.

Ther is no problem with several h2 tags on the page. Just look through wordpress templates. A lot of them have h2 tags in post title and sidebar titles.

you can have so many h2 tags as you want. There is only restriction to h1 tag.

Run your page through the W3C HTML validator.

Select the "Show Outline" option.

If the indented bullet-point list does not look like an "overview" of your document, then you're abusing the heading tags.

Thanks for this..

Ive just de-H1'd one of my sites as we had gone a little overboard with them :)