I own an S-LSA with a 912 that I fly on long cross countries fairly frequently. I have experienced stumbles several times over the past couple years. Most recently on my trip to OSH this year, I ended up having to abort and return to my home airport because the stumbling got to the point that I thought I may have to make an off airport landing. My mechanic took everything apart and cleaned it all out, changed the fuel filter and it seemed to run fine. I flew it in the AirVenture Cup race and into Fond du Lac and parked it for the week of the show. On pre-flight to leave, I found the right carb literally leaking gas out the back of the carb and the scat hose that goes to the airbox. I left the plane on the ground and had the guys from Leading Edge Airfoils come up from the Milwaukee area come up and take the carb off, replace all floats, do the complete rebuild with all new parts and replace all hoses. It ran great on the flight home from there to New York.
Bottom line is that despite the fact that I had replaced the floats per the SB earlier, the new floats were actually bad as tested by the LEAF guys. My inclination is to say it is a float related issue.