I noticed that the number of recruiter messages I get on LinkedIn was proportional to the number of replies I give to the messages in my inbox. When I'm active, I get more interest. Like, going from 0-1 new recruiter messages to 5-7 a week. Maybe I'm imagining things, but it would make sense that if you just have your profile set to "Looking for work" but you're not actually talking to anyone, you're sending a signal that you're not actively looking, and you're going to fall to the bottom of the pile. Send a few "Sorry for the delay in responding. $YOUR_PRODUCT sounds interesting. Can you tell me more," messages to the most recent messages in your inbox and see if it gets things unstuck.