I have done long rides with the bar 10+ cm below the saddle without getting a sore back, or anything. Thing is, when I do, my average speed is 2 - 4 km/h SLOWER than when I have the bar higher up.
I do know you lose power as you get lower. Weird thing with me, is that if the bar is lower than about 4 cm below the seat -- and I mean by just 5-10 mm -- my speed/power drops like a freakin' rock! (I'm talking as much as 3+ km/h slower up a 10% grade!) Any idea why such a dramatic drop in power?
My bar is only 53 cm from the seat, which seems awfully short to me, for someone who is 186 cm tall. (If I increase that reach just another 5-10 mm, I also have that same sharp power drop.) I do know my torso is shorter than normal, given my 91 cm inseam, but still. I think I have reasonable flexibility -- I can touch the floor with my fingers while bending over. I do know when I had the seat lower and/or further forward, that caused additional power loss when getting low, but I think I have the seat figured out now.
UPDATE: Today I fooled around -- yet, again!!! -- some more. Discovered that if I concentrate on flattening my back while leaning forward, I can actually go FASTER than the more "relaxed" position (when the sudden power loss occurred). (Sorry, not too familiar with anatomy . . . that's the best I can describe it.) As noted in one of the responses, this "leaning forward" motion did require moving the seat 5-10 mm forward to get to what seems to be optimal. I'll see how the "new and improved" position works tomorrow.