This is sort of wonky, but it works:

<!-- VISUALFORCE PAGE -->
<apex:page showHeader="false" id="thePage" controller="extensionController">
	<script>
		function setCookie(c_name,value)
		{
			var exdate=new Date();
			exdate.setDate(exdate.getDate() + 99);
			var c_value=(escape(value) + : "; expires="+exdate.toUTCString());
			document.cookie=c_name + "=" + c_value;
		}
	</script>

	<apex:form >
		<apex:actionFunction name="setTab" onComplete="return false;" rerender="tabpanel">
			<apex:param name="activeTab" assignTo="{!ActiveTab}" value="" />
		</apex:actionFunction>
	</apex:form>
	
	<apex:tabPanel switchType="client" id="tabpanel" value="{!if(ActiveTab != null, ActiveTab, 'tab1')}">
		<apex:tab label="TAB 1" id="object1" name="tab1" ontabenter="setCookie('apex__counter','tab1');" switchType="client">
			<apex:ListViews type="Case" />
		</apex:tab>
		<apex:tab label="TAB 2" id="object2" name="tab2" ontabenter="setCookie('apex__counter','tab2');" switchType="client">
			<apex:ListViews type="Account" />
		</apex:tab>
	</apex:tabPanel>

</apex:page>



<!-- APEX CONTROLLER -->
public with sharing class extensionController {

	public extensionController()
	{
		Cookie counter = ApexPages.currentPage().getCookies().get('counter');

		// If this is the first time the user is accessing the page,   
		// create a new cookie with name 'counter', an initial value of '1',   
		// path 'null', maxAge '-1', and isSecure 'false'.   
		    if (counter ==null) {
		        counter = new Cookie('counter','tab1',null,999,false);
		        // Set the new cookie for the page  
		        ApexPages.currentPage().setCookies(new Cookie[]{counter});
		    } else {
		// If this isn't the first time the user is accessing the page  
		// create a new cookie, incrementing the value of the original count by 1  
		    
		        ActiveTab = String.valueOf(counter.getValue());
		    }
		    system.debug('@@ActiveTab: ' + ActiveTab);
	}
	
	public string ActiveTab  { get; set; }
	

}

 Basically, every time that you change the list view, the page submits the form which causes the page to lose it's state data.  The solution above uses cookies to dynamically store that data and grab it when the page refreshes to display the last tab the user was on before the page refreshed.