I was experiencing the same behavior on multiple started checkouts.
On top of it, it seems that once 1 of the 'shopping cart' orders is really getting to a checkout completion status, the cart gets re-initialized with 1 of the other still pending 'shopping cart' orders.
From a ux perspective this can look very confusing and lead to buggy conclusions.

I think there's a way to achieve what ronmorton is suggesting by merging multiple cart orders into one order.

For another occassion, i had to execute some logic right before the first creation of an order instance.
I managed to do this as follows :

function my_module_commerce_order_presave($order) {
if (!isset($order->order_id) && $order->status == 'cart') {
// execute merge logic on other remaining cart orders
}
}

This question remains:
Do you really want to present your authenticated user with a previously started cart instance that might already be a few months old, maybe filled with products that are no longer available in stock ?
Therefore i believe cleaning up remaining order instances would be a less confusing solution from a user perspective. Can be achieved by executing the commerce_cart_order_empty() function on the remaining order instances. As such the involved order_id's are getting reused, which save us some little extra space on the database :)