This type of counterfactual history is always rather difficult to deal with, and it is doubly so in the case of Stonehenge because the monument is, perhaps surprisingly, but as I covered in an earlier answer, not very well recorded until as late as the first half of the seventeenth century.

With this said, I think that the most important factor to mention with regard to the long-term survival of Stonehenge is its geography. It is, even today, pretty isolated, particularly considering that it stands in the most densely populated, southern, part of Britain. It is around 10km (more than six miles) from the nearest large town, Salisbury. The main reason for this is that the soil in this district is extremely poor – the ground is very chalky and really it is suitable only for sheep farming.

This means that, while other ancient monuments have been partially destroyed because they were quarried for their stone – one thinks of the pyramids of the Giza plateau, which lost the external casing stones that would originally have given them a smooth appearance during the medieval period because the materials were looted for new construction in adjacent Cairo – Stonehenge was unattractive as a potential source of building materials. The sheer size of the stones, and the relative hardness of the sarsens which lie at the heart of Stonehenge, likely also deterred any thoughts of attempting to break them up for transportation to some other spot. There is a distinction to be made here with the history of the other major British prehistoric stone monument in southern England, the Avebury circle. The stones of that monument are much smaller, and the circle itself literally bisects a village, with the result that, over the years, quite a few of them have been lost, most likely to building work.

The largest building project undertaken in this district since Stonehenge was completed was the construction of Salisbury cathedral in the 13th century. The cathedral comprises 60,000 tonnes of stone, but it is built from lighter, more easily worked Chilmark stone, a calcareous sandstone or sandy limestone. Unlike the Pyramids, Stonehenge was neither big enough to provide all the materials needed for a project of this sort, nor built of the best sort of stone for the job.

One other possible reason for the reluctance to tamper with Stonehenge – much harder to assess, because it is much less written about or understood – is the reputation of the monument. Robin Fleming, in discussing deviant burials in the Anglo-Saxon period, points out how many executions seem to have taken place at prehistoric monuments, adding that "many in the tenth and eleventh centuries believed that devils and demons haunted such places." Stonehenge appears to have been of the spots used as a place of execution in Saxon times (the name itself comes from the Old English for "hanging stones", and the body of a decapitated man, apparently executed there some time in the seventh century, was recovered from a burial spot in the outer part of the circle in the 1920s). In addition, it seems to have been believed, during the middle ages, that the stones had been erected at the spot by wizardry; there was a legend that they had been flown there from Ireland by Merlin. So it seems quite possible that superstition also played some part in preserving the monument.

All this, in any case, is not to say that Stonehenge has not, in fact, been impacted by human depredation over the years. From my earlier answer:

The local people of Salisbury Plain were also interacting with the monument - generally to despoil and quarry it for homes and road surfacing, but also to chip away at the stones to carve out bits of rock that were considered lucky charms. Examination of successive images of Stonehenge show the loss of some stones and the toppling and fracturing of others, as a result of this small-scale but ongoing work. Other forces were also at work in this period, however; the loss of one 60-ton sarsen was caused by a band of "gypsies" who sheltered at Stonehenge in the early 1790s while waiting for a local fair to begin. They dug a shelter for themselves against the stone and this was enough to weaken the foundations and bring it down a couple of years later.

Sources

Burl, Aubrey. Stonehenge: A Complete History, 2006

Fleming, Robin, Britain After Rome: The Rise and Fall, 400 to 1070, 2011

Pitts, M. and Bayliss, A. and McKinley, J. and Bylston, A. and Budd, P. and Evans, J. and Chenery, C. and Reynolds, A. and Semple, S. J. (2002) ’An Anglo-Saxon decapitation and burial at Stonehenge.’, Wiltshire Archaeological and Natural History Magazine, 95 . pp. 131-146.