Narrative:

I started my second VFR flight of the day departing ZZZ to fly around ZZZ1 area. Prior to this I had just completed at 1.6 hour VFR flight from ZZZ2 in the aircraft with no issues. A normal run-up was completed with no issues detected and I departed runway xxr. While climbing past 5;000 ft.; the engine started to sputter and a drop in RPM was noticed. Preparing for a full engine failure; I completed the emergency checklist for engine failure - after which; [I requested priority handling with] ZZZ1 approach and I initiated a turn back to ZZZ. While flying back to ZZZ; the engine was still producing power and the loss of RPM returned while flying back to ZZZ. I landed with no further issues and taxied to parking. Once on the ground at ZZZ; I talked with the aircraft owner and explained what had happened. I also consulted with the CFI that had completed my flight check for this aircraft to discuss the issues encountered. The conclusion was that it could possibly be a build-up on a spark plug and it was suggested to lean the mixture to burn off any build-up before the run-up and to check to make sure both magnetos were operating properly; 2000 RPM. I was instructed to check engine temperature to make sure that the heat and high-density altitude was not impacting engine performance during the run-up - I leaned. After consulting with the aircraft owner [and] CFI and waiting two hours; I attempted to depart ZZZ for ZZZ2.I completed the run-up up twice this time to double check the mags each time. During the extended run-up there was no issues with a drop in power nor a large drop between the left and right magnetos. After not having any issues in the run-up I decided to proceed with taking off. During the takeoff roll the engine power dropped for a second; and then started to comeback. I aborted the takeoff. After the aborted takeoff I returned to the run-up area and completed two extended run-ups; one with a slightly higher RPM; 2300. I did not see any loss of power or drop in RPM during this run-up either.since no issues occurred during the extended higher RPM run-up; I decided to attempt another takeoff. After rotating to a climb attitude; the engine RPM dropped by several hundred. I pulled the power out and put the airplane back down on the runway. Once on the ground I applied brakes to stop. I came to a stop several feet into the runway overrun; [into the] gravel area. I taxied back to parking under my own power and shut down. Once back at the ramp; I called the owner of the aircraft back and let him know what had happened. The owner and a mechanic drove down to look over the aircraft and performed a long ground run-up with under cowl inspection. They grounded the airplane after finding an erratic fuel pressure issue. They parked the airplane and provided transportation for me back to ZZZ2. The mechanic's inspection the following day - 10 hours - found a boost pump with an intermittent sticky valve that allowed intermittent drops in fuel pressure to the carb at high RPM and high fuel flows. Replacement of the boost pump resolved the intermittent issue. Aircraft returned to service.

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Original NASA ASRS Text

Title: Pilot reported that during climb; the engine lost some power; requiring an air return.

Narrative: I started my second VFR flight of the day departing ZZZ to fly around ZZZ1 area. Prior to this I had just completed at 1.6 hour VFR flight from ZZZ2 in the aircraft with no issues. A normal run-up was completed with no issues detected and I departed Runway XXR. While climbing past 5;000 ft.; the engine started to sputter and a drop in RPM was noticed. Preparing for a full engine failure; I completed the emergency checklist for engine failure - after which; [I requested priority handling with] ZZZ1 Approach and I initiated a turn back to ZZZ. While flying back to ZZZ; the engine was still producing power and the loss of RPM returned while flying back to ZZZ. I landed with no further issues and taxied to parking. Once on the ground at ZZZ; I talked with the aircraft owner and explained what had happened. I also consulted with the CFI that had completed my flight check for this aircraft to discuss the issues encountered. The conclusion was that it could possibly be a build-up on a spark plug and it was suggested to lean the mixture to burn off any build-up before the run-up and to check to make sure both magnetos were operating properly; 2000 RPM. I was instructed to check engine temperature to make sure that the heat and high-density altitude was not impacting engine performance during the run-up - I leaned. After consulting with the aircraft owner [and] CFI and waiting two hours; I attempted to depart ZZZ for ZZZ2.I completed the run-up up twice this time to double check the mags each time. During the extended run-up there was no issues with a drop in power nor a large drop between the left and right magnetos. After not having any issues in the run-up I decided to proceed with taking off. During the takeoff roll the engine power dropped for a second; and then started to comeback. I aborted the takeoff. After the aborted takeoff I returned to the run-up area and completed two extended run-ups; one with a slightly higher RPM; 2300. I did not see any loss of power or drop in RPM during this run-up either.Since no issues occurred during the extended higher RPM run-up; I decided to attempt another takeoff. After rotating to a climb attitude; the engine RPM dropped by several hundred. I pulled the power out and put the airplane back down on the runway. Once on the ground I applied brakes to stop. I came to a stop several feet into the runway overrun; [into the] gravel area. I taxied back to parking under my own power and shut down. Once back at the ramp; I called the owner of the aircraft back and let him know what had happened. The owner and a Mechanic drove down to look over the aircraft and performed a long ground run-up with under cowl inspection. They grounded the airplane after finding an erratic fuel pressure issue. They parked the airplane and provided transportation for me back to ZZZ2. The Mechanic's inspection the following day - 10 hours - found a boost pump with an intermittent sticky valve that allowed intermittent drops in fuel pressure to the carb at high RPM and HIGH fuel flows. Replacement of the boost pump resolved the intermittent issue. Aircraft returned to service.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.