In reply to SafetyBod,
The Airbus system has a couple of systems that affect flap/slat retraction/extension.
For the benefit of the uninitiated, there are 2 speeds that are, as has already been pointed out, continuously computed for weight changes. "F" speed is the minimum speed for flap retraction. "S" speed is the minimum speed for slat retraction. The slats/flaps will move whenever the pilot moves the lever, however SOP is obviously to not retract until above either "F" or "S" speed, as applicable.
The first system to affect slat/flap movement is Flap Load Relief. This is fitted to the A330, and I believe, the A340. This purely inhibits flap extension when the load is too great to avoid surface damage. The only time you see this in action is when you are heavy and you select flap quite close to the Vfe for that setting.
The next system is Auto Flap Retract. This system automatically retracts one stage of flap when speed approaches Vfe, again to avoid damage. You usually see this when on a high weight takeoff, and Vfe for Flap 1+F is below or close to "S" speed. The slats never auto retract.
The last, and most relevant system to the above discussion is Alpha-Lock. This inhibits slat retraction at high angles of attack in order to keep the aircraft from getting too close to the stall.
"A pilot said Airbus planes had an automatic system which increased the plane's speed - by opening the throttle and pointing the nose of the plane down - to keep it flying if the wing flaps were retracted too early."
This sounds to me like the high angle of attack protection, which you should hopefully NEVER see, if you are flying the aircraft like any other.
I too find this report hard to believe, and would imagine that once again, facts have become distorted through misunderstandings.