I understand that we should not allow HSAs to overdraw, but does anyone know if this is an IRS regulation? If so, where can this be found?

I don't think that you are going to find anything from the IRS. It just flies in the face of the type of account it represents. As the custodian, you do have general responsibilities to properly administer the accounting for the account.

Ok - after further research the answer is definitely no:

http://www.treas.gov/press/releases/reports/notice200859.pdf

Q-35. If a trustee of an HSA lends money to the HSA, is this a prohibited transaction under § 4975?

A-35. Yes. An HSA is a plan as defined in § 4975(e)(1)(E). An HSA trustee is a disqualified person under § 4975(e)(2). A loan or extension of credit between a plan and a disqualified person is a prohibited transaction. Section 4975(c)(1)(B). Thus, any direct or indirect extension of credit between the HSA trustee and the HSA is a prohibited transaction.

And pay attention to the penalties in Q37:

Thus, the HSA stops being an HSA as of the first day of the taxable year of the prohibited transaction. The assets of the beneficiary’s account are deemed distributed, and the appropriate taxes, including the 10 percent additional tax under §223(f)(4) for distributions not used for qualified medical expenses, apply.

I have attempt to warn people about the dangers of this in a number of previous posts and so it is now official. If a bank has paid an HSA into overdraft they have voided the plan and the customer owes the taxes and I am sure that if the IRS catches on and penalizes the customer - the bank's attorney is going to suggest that they settle with the customer regarding any claimed damages. That will be on top of the penalties assessed directly by the IRS on the bank for not immediately withholding and remitting the appropriate taxes.

Good information - thanks for doing the research Randy!

Thank you for your help! I appreciate it.

Q-35 includes these two examples of extensions of credit related to an HSA.
Example 1. Bank X is the trustee of an HSA. Bank X extends a line of credit to the HSA. The line of credit is a prohibited transaction under § 4975.

Example 2. Bank Y is the trustee of an HSA. The account beneficiary accesses the funds in the HSA through a debit card. In addition, Bank Y extends a line of credit to the account beneficiary, which is not secured by the account beneficiary’s HSA, and amounts in the HSA cannot be used to repay the line of credit.
The line of credit is not a prohibited transaction.

If a bank had an LOC set up in example 2 above that could be used to fund an inadverntent overdraft on a same-day basis so that the account never had a negative balanc, do you think this would be an acceptable arrangement?

Would the same logic apply to a same-day transfer from another account at the same bank?

I don't believe so. In the example (#2), the balance is carried in the line of credit account, there is no transfer to the HSA. Once you transfer funds into the HSA account you have over contribution issues, etc.