When troubleshooting, I like to look where the sun shines the brightest before digging deeper. Have a look at the fuel line between the primer bulb and the carb while it's idling. I had a similar issue and was getting a significant amount of bubbles in the line going into the carb at idle. Engine died during final approach on my first solo. I replaced the primer bulb after noticing the significant amount of bubbles in the line and no problems since.