Hi.  I've got a mower with a Briggs & Stratton engine I picked up from someone throwing it away because it wouldn't stay running (can't find the HP or model number anywhere).  I cleaned the carb twice with no success, so I just bought a new carburetor and spark plug.  Thing started right up first pull.  However, first time I used it, it did start right up again, first pull, used it a while, then shut it off to move a chair, and it wouldn't start again.  Took off the air cleaner and sprayed some starting fluid, and after a few pulls, it started again.  Running like a champ.  Until I stop again.  Seems if I wait a day, it'll start up on the first pull again.  Definitely seems to be a fuel issue.  Air lock?  As I mentioned, it's a brand new carburetor.  Thanks for any advice!

I've seen some of Briggs do this.. 
 
However, applying the choke (yes the engine is hot)
usually gets the engine to fire up.
 
I suspect between internal engine heat(combustion chamber) and with the 
lean settings (thank you EPA) of the carb, causes this condition. 
 
See if the choke helps and advise back.
 
If it does, I'd just do that.
If it does and you want to address it, re-jetting, or opening up 
specific carb jets (richening the mix) would help..   This however
would make more carbon, and not run as clean...  
 
.

Hi,
Unfortunately, there isn't even a choke on this machine.  I've tried to add a couple photos, but that doesn't seem to be working.  Anyway, no choke.  
 


 

The butterfly, closest to the air filter IS THE CHOKE.  It's just automatic..
 
Is your carb made of black plastic?
 
**Also, as the engine appears to be a flat head, check / TIGHTEN the 3 head bolts closest to the EXHAUST VALVE.
They almost always loosen over time and does indeed make a difference in starting...
 
.

Hi.  The carb is not black plastic.  As for the choke, I thought you meant a lever or something external that controlled the choke.  It's just automatic, which is a pain.  I'll check the head bolts.  Thanks for the reply and suggestions!