Air carrier Captain reported a safe rejected takeoff executed due to an ECAM ENG 1 Compressor Vane light illuminated during takeoff roll. The Captain stated this anomaly has been a recurring issue.

Narrative

On our descent into ZZZ we received ECAM ENG 1 Compressor Vane repeatedly. The subsequent fault was written up and it was noted that in the MEL cross reference list stated No Dispatch". Maintenance came out and was instructed by Maintenance Control to perform a reset and then run the engines. The engines were both run for 2 minutes with no faults and the discrepancy was cleared. The plane was boarded and during our crew brief; the first officer and I collaborated about the fault in the event the fault came back during the takeoff. Since ZZZ is a short runway; I lined the aircraft up and held the brakes for a static T.O. FLEX thrust was applied and the T.O. roll began. The best estimate was that the fault occurred between 80-100 knots. The same fault came up as in the previous flight except line item 1 was different. The first officer read off "Engine 1 Thrust Lever Idle"; and at that time the Takeoff was Aborted.After we returned to the gate we were able to talk to the FA's (Flight Attendant) and they brought up that after we started moving they noticed a popping sound coming from the left side of the aircraft. I had the FO (First Officer) go check the #1 engine for any physical damage but he reported that that he did not see any. When serious faults that deal with major components occur; it might be prudent to take a more strict approach than just doing a soft reset and sending the aircraft on its way."