I've had a similar experience with growing parsley indoors, and I can share a few tips that worked for me.
First, light is crucial. Parsley needs quite a bit of it, so if it's not getting direct sunlight for at least six hours, a grow light might be a good investment. I found that placing my parsley under a fluorescent grow light for additional hours did wonders.
As for yellowing leaves, it usually links back to watering issues. Make sure the soil is allowed to dry out a bit between waterings, but not completely dry. I usually stick my finger about an inch into the soil to check moisture levels—if it feels dry, it's time to water. Ensure your pot has proper drainage holes, and the water isn't pooling at the bottom.
Regarding temperature, indoor parsley prefers a consistent temperature, so try to keep it away from direct exposure to drafts from windows or doors.
For soil, I use a quality potting mix that's meant for herbs, and I occasionally mix in some perlite to improve drainage. A balanced, water-soluble fertilizer every 4-6 weeks helps keep the nutrient levels steady without overwhelming the plant.
Have you noticed any improvement by adjusting your care routine, or do you think environmental factors might be playing a part as well? Sometimes moving the plant to a slightly different spot can make a big difference.