Life expectancy of a Vitamin C is 3 months once the product is opened. Once you start seeing the vitamin C's color change from light yellow to dark orange, it has oxidized. You could still technically use the product but it might not be as effective as it was.
There are some ways to lengthen it's shelf life. Make sure the packaging is air tight and kept away from sunlight. Best place to store it would be in a dark area and where temperature is consistent.
This is where your skincare fridge can come into handy! Vitamin C stored in a fridge could prolong the shelf life by quite a bit.