Yes Wine does go bad in the fridge so be sure to drink the wine up within 7 days even when it's kept in the refrigerator and make sure the bottle of wine remains sealed while refrigerating it.
Most wines will be drinkable for up to a week in the fridge as long as you keep the cork in the bottle.
After 7 days the wine begins to go bad and could make you sick so after 7 days you should throw the wine out to prevent getting sick and it will also taste bad by then as well.
After the first day of refrigerating the wine the wine begins to change taste and oxidize so by the 7th day it gets less tasty and by the 8th day in the refrigerator the wine goes bad.
The fruit character diminishes and becomes less vibrant the longer it's in the refrigerator.