Found the solution :smileyhappy:: (thanks to Sorna and Edwin)

It seems that if the component that I am rerendering has a rendered attribute, it doesn't works. So I had to wrap the pageBlockSection in an outputPanel with no rerenderd attribute. Now I just rerender the outputPanel. Attached is the updated code .

    <apex:form id="AccountForm">
        <apex:pageBlock >
            <apex:pageBlockButtons >
                <apex:commandButton value="Save" action="{!save}" />
                <apex:commandButton value="Cancel" action="{!cancel}" /> 
                <apex:commandButton value="Custom Save" action="{!saveCustom}"/>               
            </apex:pageBlockButtons>
            <apex:pageBlockSection >
                <apex:inputField value="{!Account.Name}" />
                <apex:inputField required="true" value="{!Account.AccountNumber}" />
                <apex:inputField value="{!Account.Industry}" />
                <apex:inputField value="{!Account.Has_Shipping_Address__c}" >
                    <apex:actionSupport event="onclick" action="{!changeShippingSection}" rerender="ShippingAddressPanel" status="StatusChange"/>
                    <apex:actionStatus startText="Updating page ..." id="StatusChange"/>
                </apex:inputField>
                
            </apex:pageBlockSection>
            <apex:outputPanel id="ShippingAddressPanel">
            <apex:pageBlockSection id="ShippingAddressSection" rendered="{!shippingSection}" Title="Shipping Address" >
                <apex:inputField value="{!Account.ShippingCity}" />
                <apex:inputField value="{!Account.ShippingState}" />
                <apex:inputField value="{!Account.ShippingCountry}" />
                <apex:inputField value="{!Account.ShippingPostalCode}" />
            </apex:pageBlockSection>
            </apex:outputPanel>
        </apex:pageBlock>
    </apex:form>