[Aussie Ed]

From your description of ABS / Stability control lights going off after you have driven a distance possibly indicates that you have incorrect or low tyre pressure in one wheel. Road use is warming the tyre up and increasing the tyre pressure and partially correcting the rotational diameter thus self cancelling the lamp.
So the first thing is recheck and inflate tyre pressures to correct pressure for your model (not stated). If you have been running on a seriously underinflated tyre have the tyre checked professionally for side wall integrity damage.
It is also possible that you have a lose or corroded connector to one of your ABS sensors and vibration is remaking contact and the light goes off.
If you are not mechanically capable of checking and correcting the ABS yourself, for your own safety take your vehicle to a capable mechanic.

We do not know the year or model variant of your Captiva because you havent advised us any history about your vehicle.

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[Aussie Ed]

Although probably an unlikely cause, it may be worth getting the wheel balancing weights checked just in case you've lost some weights which may affect wheel stability which may be detected by the ABS sensor(s). A worn wheel bearing can also be a cause.

Now we have vehicle information I notice that it is a 2008 model. On older vehicles it is possible that corrosion (rusting) of the reluctor rings (which the ABS sensor 'reads') can occur which can sometimes split the ring. This can give false sensing. Apart from testing the connections and the ABS sensors it may be worth while getting your mechanic to the check the reluctor rings for misalignment or damage.
The Forum Advanced Search function (three white dots to right of header bar) will list the existing discussions on Reluctor Rings.
Good Luck