Are you referring to the Fedex Ship Manager software? http://www.fedex.com/us/ship-manager/. Can you share specifics of what stopped working? Is it not printing labels any more? Or is it not writing back tracking numbers into Shopify?
Typically, external apps fail because their API connection with your store is failing. That failure could be due to authentication issues or something else. For example, our app Ordoro is a multi-carrier shipping app. We pull orders from Shopify. And then we connect to your Fedex account to look up rates and print labels. There are multiple API connections that our app monitors and manages constantly to make sure the whole system is working correctly. So, the answer depends on the details of the error you are seeing
I hope you have mentioned about the FedEx integration manager software which helps you manage shipments from your online stores in one convenient location, allowing you to see all of your orders aggregated in one location. As someone from ordoro app has stated, the external apps (like the FedEx integration manager) fails since their API connection with your store is failing, and you may not be able to get correct rates, print labels, and other functions as well. So, it is better to use an integrated Shopify app to handle the shipping.
For example, you can use the FedEx Rates, Labels and Tracking app, which will help you handle your orders from within your store. You can generate labels for all your orders in bulk, show live FedEx rates and handle FedEx tracking as well.
There has been a passage of time since you reported the issue. Hence it would be great if you can let us know what was this issue about and also how was it resolved? Ideally the cause stated here by other two people may be something which could have caused it - loss of connection with Integration manager. However, I would still refrain from speculating as i do not know the complete issue. Do let us know if you can provide some info as it would help others who are facing the similar issue.