Yes. It is recommended to keep Sangria refrigerated at all times.
As explained by WineIntro, Sangria does have some alcohol in it, so it isn't likely to become "poisonous". However, it has wine and fruit in it, and these things tend to decay in warmth. Wine becomes vinegar rather quickly once exposed to air. Fruit of course gets mushy and fall apart. It's really in your best interest to keep your Sangria in the fridge at all times and use ice cubes when it's out on the table.
Sangria is a beverage, common in Spain and Portugal. It normally consists of red wine, chopped fruit, a sweetener, and a small amount of brandy.
Easy to make and drink, the fresh seasonal flavors of sangria are pitcher perfect for summertime gatherings. Check out 17 Best Sangria Recipes from delish.