There is a setting that can easily be changed to retrieve orders that are from more than one day ago.
For this example, we will use the Amazon Seller Central order import.
If you go to the Import Orders (File>Import>Import orders), once you are on this dialog; select your order type to import and click 'Edit'.
The Order Import Information dialog will pop up, if you then go to the 'Get orders from Amazon SellerCentral Website' you will see the 'Order Reports' section to the right.
Under the Order Reports you get the option to change the amount of days you want OSOP to retrieve orders from. The default setting for this is one day, so if you wanted to retrieve orders from a week ago, change this figure to 7.
By changing the amount of time you retrieve orders from, this will not affect or overwrite any orders already imported.