Are there grounds to bar a soldier from reenlistment if they are dismissed from BLC due to academic deficiency?

Bar to Continued Service is imposed for failing any NCOPDS for any reason.

Absolutely. It is required by regulation to bar a Soldier for failing any aspect of an NCOPD course, and your promotable status will be revoked as well, as you failed to meet the requirements for advancement.

As for you being able to return, that depends upon your Chain of Command. And the reason why you failed.

As 1SG Bradshaw stated, a bar to continued service will be imposed if the individual fails for any reason (any of the phases). However, you can still attend BLC but will need Higher approval from your first General Officer. Also it depends on if the individual failed slightly or did not do anything during that time.

AR 601-280 requires a Commander to impose a bar for failure of an NCOES. Of course the bar has to be removed for the Soldier to re-attend the NCOES. The Soldier may return to NCOES at a later date, but it requires a signature from your Commanding General to endorse your request

Don't ever fail.

Yes. As has been stated any failure results in a bar. The key word you seem to overlook is "able," meaning that if the SM proves sufficient worth to the commanding general that they can re-attend.

The larger question would be why you failed the academics in the first place? The course is designed to be challenging, but passable. The Army sets you up to succeed but requires good faith and diligence on your part.

Not only is this in the regs, as already pointed out here by many, it would be spelled out in the welcome letter or LOI that the Soldier received either before starting or first day. It's part of the in processing packet that hardly anyone ever reads before they sign

Yes. Depending on the reason for failure from an NCOES you can retry a few months out or 6 months later. Just do it the first time and you won’t be in this situation.

If you fail BLC then you can expect a bar to re-enlistment. That said, if you can get another bite at the cherry before you ETS and you pass, the bar will (probably) be lifted. The only problem is that the second bite is notoriously difficult to get because you need the Brigade or Division commander's approval. Finding a way to Show you have corrected your deficiency could help.
By far the biggest hurdle is the General. He will likely ask the CSM's opinion, which he will form by speaking to your leadership. If they're on your side it may help. If they're not, you're sunk.

Simply put - I would certainly hope so.