How many corneys can you carb?

Today is a dark day. I woke up to my co2 tank empty. This is after only one keg carbonation and emptying, and a second keg about halfway there(all at 12psi). My tank is 7lbs and I feel like it should be able to carb and propel more liquid. How many kegs should I be getting per tank(approx obviously)?
I use a picnic tap, I left it attached to both kegs, would this cause a gas leak? I don't think I have a leak anywhere else(using 5/16 barbs(I think) for 1/4 hose with clamps, so its super tight.)
Should I go somewhere else to fill my co2 if I was hypothetically leak-less?
Also I would turn on and shut off the gas after the beer was carbed to pour beer,is this inefficient?
And finally, when I turn the valve on my tank, at certain points, I can feel a very light spray of air coming from the valve(like 1/2 of every turn) is this normal or is there a leak in my tank?

The only way to know for certain you don't have any leaks is to use some soapy water on each and every connection you've got (keg posts, any hose connections, around the regulator, at the taps, etc.). On a 5lb tank, I was able to force carb several kegs and serve about 4-6, I've lost track. But 1.5 carbed and 1 served is not right.

yea, I just ran some gas into the first keg I used. I had a leak when the lid faced one way but not the other. I suppose that could be it(but I'd like to think I would have noticed it). I'll have to test all my other connections when I get my tank refilled.
Any insight on the picnic tap? Should I unplug that after I use it or is it ok to leave hooked up?

Those darn kegs and lids can be very fussy. I agree, the soap and water is a good trick. I also try and go some place quiet and put my ear right next to the thing. I look like an idiot but it's a great way to listen for leaks.

You'd be surprised where it can leak from: the lid seal, relief valve, gas post, gas fitting, liquid post, liquid fitting, hose connections, regulator, etc.

I've had the sunken heart feeling of an empty tank, and it sucks. With a 7 lb tank, I would guess you should be getting close to 10 kegs or more (carb and serve), so obviously there is a problem. Leaving the picnic tap in shouldn't really cause much of a concern.

I'm on keg seven with a 5gal tank. Carbing at 30 psi for 48hrs then running about 10-14psi

I had this same problem with my 5lb tank at first, and my solution was to seat the seals by blasting the kegs with 30-40 psi initially to be sure they sealed. Then I found that one keg only sealed with the lid in one direction (weird I know), and finally I found that 2 of my pressure relief valves were going bad, so I replaced them. worked like a charm, I've had the same tank for a couple of months now, and it hasn't run out. I've done at least 4-5 kegs on it, so I think my problem has been solved.

keg lube works wonders on the gaskets and poppets. And like that Bigjerk said properly seating the gaskets with high pressure really helps.

I lube all the poppet and O rings after each cleaning. Also I force carbed the first keg at 30psi so I feel like it would have seated =(