Lawn-Boy Starts, will not stay running?

I have a 2005 lawn-boy 10685 with the Tecumseh engine. It will start (only if you prime it), and run for 10-15 seconds and then die. You have to prime it again to get it to start.
I've replaced the spark plug, verified the gap (.030), changed out the fuel, changed the oil, and so on. I even tried it without the gas cap just in case it was a bad cap.
Today I pulled the float bowl off and cleaned it, then pulled the carb off and thoroughly cleaned it. I found one dog-ear on the intake pile was broken, so I repaired it with some "magna-steel" putty it, grinding down and smoothing the epoxy once it set hard. It's solid, and I've ordered a replacement pipe anyway (2 weeks or so to get it). Then I put it all back together and it has the same exact problem... So, with cleaned out jets, cleaned bowl, new spark plug (again), you still have to prime it, it will fire up immediately, run for 10-15 seconds, then die.
I had assumed that the cracked pipe would be like a cracked intake manifold for a car, but the putty really did seal it hard, so now I'm scratching my head. I tested the spark against the block, that's fine. So I'm thinking that it's fuel-flow related, and I just know I'm staring right at it and not seeing it. Only other thing I can think of is that for the few seconds it is running, it seems to be self-adjusting the throttle up and down, like it's trying to stay running....

What am I missing?