This is a design feature, it is a common desire to simplify the checkout funnel by not distracting the user with extraneous links. Once they are in the cart we want them to stay there.
This might take some CSS styling, but the beginning point to stop this behavior is in
/common_files/customer/content.tpl:
HTML Code:
{if ($main neq 'cart' or $cart_empty) and $main neq 'checkout'}
<div id="left-bar">
{include file="customer/left_bar.tpl"}
</div>
<div id="right-bar">
{include file="customer/right_bar.tpl"}
</div>
{/if}
See the {if} statement there? Removing it should do the trick. Make sure to get both sides, remove {if ($main neq 'cart' or $cart_empty) and $main neq 'checkout'} and the closing {/if}.