Host complaining about too many HTTP connections, fix it, or find another host?

The tabs and dropdown menus are done using jQuery UI (http://ui.jquery.com/). Take a look in the page source, the scripts are in the head.

For the tabs I had to rewrite a function in template.php to return a unordered list of all blocks before returning all blocks:

/**
 * Return blocks by region as panels
 *
 * @param $region
 *	 The template region to fill
 */
function stylos_blocks($region) {
	$output = "";
	if ($region == 'right') {
		$tabs_array = array();
		$panels = "";
		if ($list = block_list($region)) {
			$i = 0;
			foreach ($list as $key => $block) {
				// $key == <module>_<delta>
				$anchor = "#block-" . str_replace('_','-',$key);
				$tabs_array[$i]['title'] = "<span>{$block->subject}</span>";
				$tabs_array[$i]['href'] = $anchor;
				$panels .= theme('block', $block);
				$i++;
			}
		}
		$tabs = "<ul>";
		foreach ($tabs_array as $tab) {
			$tabs .= "<li><a href=\"{$tab['href']}\">{$tab['title']}</a></li>";
		}
		$tabs .= "</ul>";
		$output .= $tabs . $panels;
		
	} else {
		if ($list = block_list($region)) {
			foreach ($list as $key => $block) {
				$output .= theme('block', $block);
			}
		}

		// Add any content assigned to this region through drupal_set_content() calls.
		$output .= drupal_get_content($region);
	}
	return $output;
}

We just got another e-mail from our host.
After inspecting the logs, I realised that a lot of hits seems to come from search engine robots, can that be the problem?