Eggplant usually last in my fridge for about two days before I cook it without any problems.  I tried going four days once because I ended up going out of town and that didn't work out so well.  Also, after you cook it, it usually last me about a week and a half for recipes like Baba Ganouj (eggplant hummus) and about 4-5 days when made into my version of Eggplant Parmesan.  You might want to keep your eggplant in an extra cold area of the fridge for the same results, I tend to keep my refrigerator on the cold side-then again, I live in a rural town in the middle of nowhere, so I'm sure that eggplant from a farmer's market would be way more fresh than I'm use to having!

I've had an eggplant in my fridge for 1.5 weeks in the past and ate it and it was just fine! You do not have to worry about a thing!