I apologize for any generalities, but this is a very broad question. The two main reasons for this are due to how armies were raised and how battles were fought.
How armies were raised:
Despite the obvious ubiquity of stones throughout Europe, there are only a few places that substantial parts of the population trained to use slings, which like many weapons developed as a tool for hunting that was then utilized for warfare. Generally slingers could be found on rocky Mediterranean islands such as the Balearic islands or Rhodes. But for those slingers to actually take part in warfare on a scale worthy of being recorded in chronicles, someone had to go to those places and hire them as mercenaries. And the use of mercenaries in European warfare in general was far more common in antiquity than during the Middle Ages, mostly because the great empires of antiquity were far more powerful than any kingdoms of medieval Europe. Athens, Macedonia and their successors states, Carthage, Rome all had the resources to afford to hire mercenary slingers as useful additions to their professionalized armies. On the other hand, the armies of medieval France, England, German principalities etc. had much less central power and thus revenue to hire mercenaries from far-off lands. This is not to say that no mercenaries fought in the Middle Ages, just that their were fewer and they were more likely to be recruited locally. And of course, once you get to the 15th century (the Early Modern period) this entire trend reverses and mercenaries start to become more common again, as medieval kingdoms slowly start to condense into the nation-states of modernity. But by that point mercenary companies are primarily pikemen (such as the Swiss companies or the Landsknechte) or free lances.
How wars were fought:
To bridge my two sections, it's important to note that while slingers are very effective against lightly-armored enemy skirmishers, they are not so useful against cavalry, who can chase them down and are less vulnerable to their missiles. Thus even before the sling as a weapon was made obsolete by the spread of gunpowder, it was not particularly useful in the Middle Ages, when the dominant battlefield force were mounted knights.
But relating the "battlefield" itself as the place of medieval warfare is not very accurate. Yes, set piece field battles did occur in the Middle Ages (Hastings, Crecy, etc.) but they were not nearly as common as in Antiquity, and none of them were on the same scale. While Hastings involved perhaps 20,000 combatants in 1066, Zama in 202 BC had involved 75,000 (including Balaeric slingers in Hannibal's force). While ancient wars between large empires were often settled on the field, medieval warfare centered around sieges. And slingers are not very useful in a siege on either side. Castles were designed with slits for use by archers/crossbowmen, who could fire their weapons while remaining mostly in cover, but a slinger can't really use an arrow slit, and even if they are on the top of walls they are still made less effective because the use of a sling requires a lot of open space (And of course, from that height you may as well just throw rocks at people below). And on the besieging side, missile-armed warriors aiming up at the defenders really preferred to be behind some kind of cover, but again you can't really fire a sling from behind a pavise or a guy with a shield.
EDIT: here's a journal article that goes into more detail on the use of slings (with citations), I hadn't seen it before writing my post but in general we were thinking along the same lines. The most important things to note that I don't get into are his emphasis on the importance of training from youth in the use of a sling, the decrease in its civilian use due to medieval urbanization (and the recruitment of mercenaries from urban environments) and the near impossibilty of using a sling in tight medieval formations or as part of volley fire. http://www.chrisharrison.net/index.php/Research/Sling