Should a supervisor get negatively counseled if their Soldier does not make progress from an ABCP or APFT failure?

I wouldn't counsel for one Soldier/NCO not maintaining standards, but if the Soldier was not counseled/recommend for a bar to reenlistment, OR this became an issue through the squad/section without intervening, the leader must be held accountable.

There are a couple of things you have look at. First is the rank and experience of the person who failed. If it is a mid-career NCO, I would tend to put the onus on that Soldier for the failure. If it was a junior enlisted, I would look at the leadership. When there is a problem, I try to see what leadership failures happened and correct those if I find them before I do anything else, especially when I look at the subordinate's experience and knowledge level.

It depends. If the senior leader does nothing to address the performance issues then they are not doing their job and should be counseled. However if the senior leader is doing what they need to do and the individual doesn't perform then no they should not be counseled. At the end of the day the NCO is responsible for everything that happens or fails to happen within their area of responsibility.

No, nutrition is a big part when dealing with weight loss and you really can not monitor what a Soldier puts in their mouth. You can work out with the Soldier and go with them to the sauna but if the Soldier goes and eats a 3000 calorie meal when your not around. Soldiers need to learn accountability and be able to police it up themselves and if they can not or not willing to than they should be put out.

what's the whole story here?

In a perfect world the answer would be no but in the real world that we live in the answer is yes. The primary reason progress wouldn't be made after full knowing a soldier has struggled on an APFT or ABCP is because he/she was neither properly counseled or remediated. Now if this has been completed we go back to the perfect world scenario. We don't live in one and from day one as an NCO you have agreed to take responsibility for said soldier. The fact that the soldier was going to do poorly on the testing should have been able to be seen and noted prior.

Depends on what the supervisors plan of action was and if it was followed, if there was a solid POA and it was followed then the answer is NO.

Counseled- yes, negatively counseled- it depends. The supervisor should be formally counseled regularly, and as a supervisor, part of that performance regards their leadership/ mentoring abilities. Counseling should also include suggestions on supporting the subordinates.
Any negative counselling, regarding non-improvement, should be when little or no real effort is made by said supervisor to help, guide, or aid subordinates.

Only if the leader can not demonstrate that he/she did nothing to help the soldier improve.

This begs the question: was that soldier's failure at least in part due to the NCO's negligence or incompetence? If not, then the soldier should stand or fall on his own account. There are some soldiers who will not respond to even the most expert of leadership. On the other hand, if the answer is yes, then both the soldier and the NCO deserve reprimand.