If you're only using it for potatoes and nothing else, AND if you strain it at the end of service each and every day, you should be able to get 5-6 days out of it. A lot depends on fryer temperature and usage. Duck fat has a tendency to break down quickly at higher temperatures.
When using it for duck confit it can be re-used many times because it's cooked at a low temperature. Only experience will teach you how far you can go with this. Your eyes and nose will know when.
Often you simply have to track the fat daily and test your product. Keep a simple log and you will get a feel for how long the fat will last. I agree with @Chefross if you are just frying potatoes then you should get several days out of it.