If I understand wind-chill (which I probably don't), the air feels colder because your body doesn't have as much time to heat the air as it passes by. But in that case it seems like there should be a wind-speed at which the amount by which the air is heated by your body is 0 (or negligible). At that point you're feeling the "actual" temperature the air is at. How much temperature difference would that speed be from no-wind? What wind-speed is that?
No there is no limit to the math of wind chill, though there is a maximum wind speed that has ever been observed.
Here is what wind chill is. Imagine you have a hot cup of coffee. You can leave it at room temperature for a while and it will cool down to where you can drink it. Or, you can put it in the fridge and it will cool faster. Or put it in the freezer and it will cool faster still. (People are more complicated because we don't really cool down, assuming we're alive, but we lose heat by being in the cold.) So you have these three temperature differences between the coffee and its environs and three rates of cooling. Or, you could blow on the coffee with your body temperature breath and actually cool it faster. If blowing cooled the coffee at the same rate as the fridge, being blown on while at room temperature would "feel like" being in the fridge for the coffee.
Wind chill says "at A degrees, a person will lose heat at rate B. At C degrees with a wind speed of D, they will also lose heat at rate B. So when the wind speed is D, they say "it's C degrees but with the wind chill it's A." The numbers they use come from observations of actual humans, not a mathematical model of heat loss. Specifically,
The wind chill index is based on the loss of heat from the face, the part of the body that is most exposed to severe winter weather. Volunteers were exposed to a variety of temperatures and wind speeds inside a refrigerated wind tunnel. They were dressed in winter clothing, with only their faces exposed directly to the cold. To simulate other factors affecting heat loss, they also walked on treadmills and were tested with both dry and wet faces.
To ensure that the wind chill index met the needs of Canadians, Environment Canada conducted public surveys across the country. The current index is expressed in temperature-like units because it is the format that was preferred by most Canadians. However, since the wind chill index is not actually a real temperature but rather, represents the feeling of cold on your skin , it is reported without the degree sign.
You can calculate it yourself online, and that page has a button you can click to see a table also. The table doesn't really "level off" or flatten off, but it only goes as high as the wind is likely to get to. The page explaining how it's calculated concludes:
Where is the coldest wind chill in Canada?
Wind chills below -70 have been recorded in northern communities in Canada. On January 13, 1975 at Kugaaruk, Nunavut, the air temperature was -51°C and the winds were 56 km/h, producing a bone-chilling wind chill of -78!
Wind chill factors verge on being junk science, especially when interpreted uncritically. However, your physical intuition does make sense, and published formulas and tables do have a property very much like the one you have in mind: as the wind speed increases, the incremental effect of adding a given amount to the wind speed gets smaller and smaller. For instance, some common formulas for wind chill have an effect proportional to v0.16. The fact that the exponent is so close to 0 tells you that the graph of wind chill versus wind speed is very steep at low speeds but bends over and becomes very flat at high speeds. For example, when v goes from 5 mi/hr to 10 mi/hr, v0.16 goes up by 12%, but when v goes from 55 mi/hr to 60 mi/hr, v0.16 goes up by only 1.4%.
Your understanding of wind-chill is a bit confused. The reason the wind feels colder is because of convective heat transfer. When there is a difference in temperature between two objects, thermal energy transfers from the hot to the cold. In the case of a person in the air, the thermal energy flows into the air, and the faster the air is moving, the more thermal energy can be drawn out of a person.
Just like how a car radiator fan turns on when the engine is hot, by moving more air over the radiator, more heat transfer can take place.
The actual math of convective heat transfer is rather complicated, and so wind chill is a term created to simplify the concept and make it easy to digest in terms everyone is otherwise familiar with.