How long have I got, doc?
How long does it take for good fry oil to turn bad you mean? That depends on a number of factors, chief among them the type of fat you’re using. In general, you want one that’s fairly stable (i.e. resistant to breakdown) and neutral flavor-wise. For me that means either vegetable or canola oil. Solid fats like shortening or lard are even more resistant to breakdown, but are less convenient for the home fryer.
Assuming you don’t fry a whole lot of food at one time, you should get half a dozen uses out of a single pan full of oil (you’ll have to replenish some of course, since the food will soak some of it up). But use your nose. If the oil looks dark and/or has that telltale fishy ketone smell, dispose of it. You can do what I do and pour it out in a remote corner of the yard, or put it into disposable vessel and put it in the trash. Under no circumstances put it down the drain. Even liquid fat is hell on pipes.
Another important tip: if you want to re-use oil, don’t fry in an uncoated cast iron pan. Exposed iron acts as a catalyst that speeds up oil breakdown by many orders of magnitude. I know, grandma made fried chicken in that big cast iron pan you have. There’s no reason to break tradition, just don’t expect to use the oil again afterward.