A319 Captain reports Autothrust operating inappropriately during visual approach to DCA. A thrust addition occurs with aircraft speed above magenta speed bug setting of 131 knots. Autothrust is switched off and normal landing ensues.

Narrative

Cleared for Mt. Vernon Visual Approach to Rwy 1 at DCA; Autopilot off; both Flight Directors off as per company procedures. Approach mode had been activated and confirmed. On profile at approximately 180kts; Flaps 2. Selected managed speed upon command of Pilot Flying. Airspeed bug changed to magenta and drove to 131 kts. This was off scale low so we got a 131 at the bottom of the airspeed scale (Vapp on FMGC was 129). Extended gear on F/O's command. Thrust started to increase slowly for 1 or 2 seconds; then more rapidly. I was Pilot Monitoring so I checked FMA. We were in Speed mode with magenta 131 airspeed bug. Thrust should have gone to idle to slow to 131; but was increasing. F/O disconnected Autothrust to prevent flap overspeed and used manual thrust to an uneventful landing. F/O and I have been on the Airbus for many years and could not explain why this happened. It has been our experience; and common knowledge on the line that as our aircraft age; it seems some aircraft do not do as good of a job at holding airspeed as they used to; both in autothrust speed mode and autopilot pitch mode. I can only assume this was a mechanical malfunction.