Our bodies weren't made for extended periods of time upside down. There's a reason that our lungs sit on top and it has to do with how they'll get squished by all the bigger and heavier organs once you're upside down. At some point your lungs won't be able to absorb enough oxygen to keep your body alive.
This might possibly be one of the worst ways to die as it is a very excruciatingly long suffocation. And this isn't even accounting for how hanging upside down for a very short time will cause you to feel like your head might explode or your eyes might pop out. This feeling definitely won't lessen over time and must have been felt by the Utah man who died after hanging upside down for 28 hours inside a cave. It's almost as if Death put you on the waiting list just to make you suffer longer. You'll realize that your running out of oxygen but this feeling will continue on for hours until your body finally gives up.
Brief periods of upside downness can actually give some really compelling health benefits. Being upside down, helps the blood flow from your legs and feet back to your heart where it can pick up fresh oxygen. Over time it can lower your resting heart rate (your heart works more efficiently) and thus increase your overall endurance.