C152 pilot reported their rental aircraft engine ran rough and quit during runup and they returned to the FBO. Reporter stated the FBO did not take the aircraft out of service.

Narrative

I rented the plane for a flight to practice maneuvers. I found no abnormalities in the preflight inspection; oil was at normal levels; both tanks had almost full fuel; and the engine heater had been plugged in. OAT was about 10 degrees C. The engine started normally; oil temp and pressure were normal. I taxied for a runup and began the checklist. The engine had been running for about 3 minutes when I advanced the throttle to 1700 RPM. The engine ran moderately roughly when advancing the throttle. I verified that the mixture was full rich. I checked the left magneto and observed an RPM drop of 200-300 RPM. The right magneto dropped about 100 RPM; which is within normal limits. I wanted to clear any fouling on the spark plugs; so I advanced the throttle to 2000 RPM on the left magneto only; and the engine ran very rough. I began to slowly lean the mixture; and the roughness continued; with RPM quickly dropping to around 1500 RPM. I enriched again to full rich; and the engine continued to sputter. The aircraft was shaking to an extent that instruments were unreadable. With the mixture on full rich and L magneto still selected; the engine died. It seemed mostly shut off; except the propeller still 'coughed' as it does when initially cranking during a cold start. I pulled the mixture to idle cutoff; and the engine shut off within 5 seconds. I turned off ignition and master switches and contemplated for a few moments to decide whether to taxi the plane back to parking or leave it there. I decided to restart and taxi to a parking spot so it would not obstruct the ramp area. The engine ran slightly roughly while taxiing; I did not perform another runup. I returned to the FBO; reported the engine failure; and completed the appropriate paperwork. I was informed by an instructor about 1 hour later that the problem could not be reproduced; and the plane was remaining in service. I think this is a safety issue because there was a clear problem with the magneto; and the engine showed clear signs of abnormal operation. I overheard the chief instructor ask if I was sure the mixture was full rich; so I stepped in to confirm that I had verified the mixture setting. Overall; there seemed to be doubt about my report; and I think it is unsafe that the plane was returned to service without a mechanic looking at it. I have reported other engine issues with this FBO's planes; and I do not believe that my reports were taken seriously. One time; I aborted a takeoff due to engine issues; and I did not observe any corrective action taken by the company in response to my report.