The problem is that on a desktop browser the user can simply hover the mouse over the menu to make it appear.
On a touch screen device, they can't do that. When they tap one of the drop down headings, the browser follows the link as defined in the page:
e.g.
Code:
<li><a href="/myblogs">2010</a>
If you remove the <a> tag then what you want
might start working again, but you'd lose the ability to go to the main page for each category.
You could add the main page for the category to the list itself so that it can then be chosen by the user.
There are probably also other JavaScript libraries that will work around this issue.