I've had problems with the plastic part that feeds into the carb you're talking about falling out of the carb too. What I do to avoid the situation altogether is before I even run an OS 15 LA for the first time I really go through it to avoid some of the weaknesses in the engine. One thing I do which has solved your problem is I put JB weld over the joint where the black plastic part joins with the carb. This will prevent it from slipping out, which it will invariably do with time. I also replace the plastic backplate with a metal one, sealing it with hi-temp gasket goo (I forget the name at the moment). I also replace all the screws in the head, backplate, muffler, and carb with socket head bolts so I can remove the screws easier with an allen wrench if necessary. Drill out the baffle to increase RPM's. A lot of great tips on break-in procedure, etc can be found at this website: http://www.georgiacombat.com/OS15EngineSetUp.htm That website has been REALLY helpful to me.
Hope that helps,
Dr. Andy Runte aka "Dr. Kamakaze"
of -TEAM KAMAKAZE-
RCCA #876
AMA #273119