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

I don't think they should you can take a horse to water but you cannot make it drink it same with abcp or the apft

Depends.

Once a Leader is made aware of an issue, they are responsible for "doing everything within their power" to correct said situation. However, ABCP & APFT failures have very specific "programs" for correction that must be adhered to. The Leader must enforce said programs (duty of an NCO), but personal accountability comes into play for "progress."

If the Leader is enforcing the program as written, what is the cause for negative counseling? If he is not, then absolutely.

When we start adding "punishments" for things that are nominally outside the (regulatory) control of the Leader, we run into a Conflict of Interest. Does the Leader adhere to the Regulation, or do they attempt to protect their career and deviate from said Regulation by doing what "they think will work best" (even though the Service has a defined process)?

That does not mean we cannot used "event based counselling" (neutral) as a learning experience, but we must be cautious not to place our people into ethical dilemmas.

My initial reaction is no.

However, depending on observation of the supervisor's actions between tests, it could be a yes. Is the supervisor actively encouraging the subordinate or just telling them they need to pass? Does the supervisor often go out with the subordinate to all you can eat buffets or bringing in donuts every morning?

Overall the performance is the individual's responsibility. The leadership i what should be addressed if there are situations akin to what I described above.

The Three Meter zone gives great clarity for focus on why most soldiers fail the apft in the first place and is worth a read.
Personally, I agree with all of the above, the soldier will go where the NCO leads them, but if the leader isn't doing it right, then you're (the blanket you) just as responsible for leading the soldier down the path of failure.

I hope you get them back on track.