The best solution is to use a heavy pot that retains heat, which is why I recommend an enameled cast iron dutch oven. If you don't have one, you can heat your oil to closer to 400°F to combat the severity of the temperature drop. Make sure you're using a high heat oil if you need to do this, Canola oil, Safflower oil, Vegetable Oil, or Avocado oil are good examples of oils that won't smoke or burn at this temperature. You can also turn up your burner once the oil has dropped to maintain or return the oil to temp. IF needed, cook the Brussels sprouts an extra minute or two to ensure they're cooked..