My gymkhana mare does the exact same thing when she’s winded. She pulls her head down at the lope and nearly drags the ground with it. It is extremely un-nerving at that speed. She never has an issue with it if it’s a short run, but if I’m pushing her for any distance her head goes straight down once she starts getting tired. I’d stop him and let him take a break if you think it may be he’s getting tired, especially if he’s breathing hard. I also agree with pheets. It may be that he is simply unused to working the muscles your asking him to use so even though he may not be tired his muscles are starting to hurt. Let him rest, horses generally do what they do for a reason, listen to what he’s saying. If it’s a fitness, conditioning issue he will get over it as you work him more.