Assuming you're using one of the commercially available saddles like an Aerohunter or a Mantis there would be about a dozen things that would need to fail catastrophically before you actually fell out of the tree. That is if you're using the product(s) as intended.
There's a lot of redundancy inherently built into saddles - from the rigging hardware to the knots that are used.
But let's assume you're all setup at hunting height with one of the commercially available platform options (WE stepps, bullman steps, or predator platform, or screw in steps). We'll start from head down.
At about head height you would have your tree tether. The commercially available ones use climbing rope with high dynamic load rating and usually come with a prusik knot or blakes hitch, and a rated caribiner. They either have a spliced eye or a with a figure 8 knot to girth hitch to the tree. One the tag end there is usually a stopper knot. In the middle is your prusik or blakes hitch, with your carbiner. So 4 things would have to fail on the tree tether alone before you even get to the saddle: The figure 8 / eye splice, the prusik knot, the carbiner, or the stopper knot. That's 4 just on the tether.
Then we get to the saddle. We're clipped in on the bridge with our caribiner. That's 1. The bridge is attached to heavy duty bridge loops on either side of the saddle, either with knots or spliced eyes. 4 more connection points. Then the linemans belt can be kept in play too. Linemans belt is attached to heavy duty linemans loops via knot or splice, and uses a carbiner on one end to attach to opposite side linemans loop. On the linemans belt itself we have 6 different things that would have to fail: linemans loops x 2, linemans knots, caribiner, and rope itself. That's 5. So on the saddle itself there are potentially 10 things that would have to fail before you fell out of the tree.
I'm not going to count up the platform points, but by my count there are at least a dozen different things that need to fail before you can even start falling out of the tree. Of course chit happens and all that, but there is a LOT of redundancy built into saddle hunting already. They are very safe if used properly.