Supposedly, some form of depletion (and recovery) feature will come in a later version, so overmining a certain planet will result in significantly reduced profits.
However, this doesn't affect asteroids; it would be a bit of a waste to store depletion ratings for so many of them; so how about a few more proposals?
1. "Large" asteroids i.e. the ones you can land on in the map, are set to have a finite number of random resources, generated when you first "scan" them. Your mining stat then determines how many of those resources you can get per mining cycle. When the resources are gone, the asteroid is removed from the map. To compensate, they have a chance of a cache (which is significantly larger than a random cache finding in regular moon/planet mining), which you reach after you fully mine the asteroid.
2. If you've played in non-Corvus mode, you've seen those randomly generated asteroid clusters. Perhaps make it a large clickable object (like a moon). When interacting with one, you can then "search for an asteroid" which - after passing some time on the overmap - will then randomly generate a mine-able object. Searching for an asteroid has a small chance of an accident; both to simulate bobbing and weaving through an asteroid field and stopping players using it endlessly. When searching for asteroids, a high sensor rating improves the yield of the randomly generated object and reduces the chance for accidents.
A mine-able asteroid generated this way will have a random yield (like how current mining works), a random danger rating, a chance for a single cache, and a random size. Size determines how many times you'll be able to mine that particular asteroid before you have to look for a new one. If you don't like it, you can search for another one. If you leave before the asteroid is fully mined out, then it is lost regardless of remaining chances.
While both searching and mining in an asteroid cluster, your sensor profile and sensor rating is reduced, to simulate the interference of being in an asteroid field (This doesn't affect asteroid searching).
3. One last thing to consider is caching mined resources. Right now, we can't exactly control how many resources we get from mining which can easily put us over capacity. With depletion vastly reducing the gains; it would be nice if planets, moons, and possibly asteroid clusters can have an interactive empty market. If you want to balance it, perhaps give it a chance of losing items over time.