First of all, thank you. I just hope I can do Mike justice here.
The roundworms can play a roll here. They can cause diarrhea and vomiting in young animals. How long ago was he treated for that?
As far as expecting too much from him, I'm not to worried about that. From the moment puppies are born, they are taught the rules of the pack from their mother. The main thing that humans have to worry about is not being able to find the balance between being calm and correcting the behavior.
You remember watching the "Set it and forget it!" infomercials? That's the approach you need to take with all corrections "Correct it and forget it!" If you've got him on leash, then a gentle tug coupled with the stern "NO" will be all you need. Remember, the purpose of the correction is not to punish, it is to redirect the dogs attention to you.
Now onto your issue:
First, is there just one spot that he goes in when he's inside? I'm sure you're probably doing this, but you absolutely have to make sure that when you clean up the mess, that it is totally clean. Dogs experience the world with their nose first and you have to make sure that the smell is totally gone.
Second, has he done it in the kennel recently?
Third, Can you think of anything that would link the accidents together? Is he excited? Are you excited? Is it before or after you do an activity? Is it before he gets fed? etc...
Since he's a young, energetic puppy, it would benefit you both to work on training patience. This is going to help his attention span issues, which may, in turn, help the accidents too.
Your job is to create associations for him. You want to start associating everything with relaxation. Starting thinking in his terms, everything has a meaning. Change feeding time to a feeding ritual. The bowl does not get placed on the ground until he is calm and relaxed.
When you get home, he doesn't get acknowledged until you are ready and he is calm and relaxed. I think you can see where I'm going with this. What this will start to create for you is the ability to see changes in behavior easier.
If he is relaxed, then out of the blue he starts to sniff around or whimper, that's a sign that something is going on.
Couple that with keeping him tethered to you should start to see some results.
On some other notes, how well are the walks going?
and also, you broke the cardinal rule! We need pics of the little guy!!