Every so often, Amazon's authorization token expires, which takes away InventoryLab's access to your Amazon account.
Re-binding your account to Amazon's MWS should solve your problem! It's easy to do :)
Login to your InventoryLab account
Click your name in the upper right hand corner and select My Account from the drop down menu
Click Amazon MWS ID from the menu on the left
Click the Bind Automatically button
You will then be taken through a short binding process with your Seller Central account which, at the end, will put you back into InventoryLab.
Please allow 24 hours for any missing data to sync to your account if you have any, but you should be able to Search and List within about 15 minutes.