IRS rules state that HSAs can cover premiums for continuation coverage, like COBRA. Although the premium payments during unpaid leave are not COBRA, they do act as continuation coverage.
A literal reading of the law (Section 223 of the Internal Revenue Code - https://www.law.cornell.edu/uscode/text/26/223) would suggest, "no".
The law allows for 4 situations in which you can pay for health insurance premiums from your HSA:
***Notes***
(i) refers to Cobra coverage.
(ii) refers only to LTC.
(iii) requires that you qualify if you are actually receiving unemployment benefits.
(iv) refers to people 65 and older.
So what you need to do is go to your benefits co-ordinator and see if (i) or (iii) can apply to you, since I do not know the details of what your "leave of absence" are. Show your benefits person the wording of the law to help him/her understand what the requirements are (this can be a bit different than the IRS instructions).
The reason that I supplied the wording of Section 223 is because I am a tax professional, not a labor law professional - that is, I do not know all the cases in which "any" Federal law requires the continuation of coverage during your "unpaid leave". I also don't know if you are eligible for unemployment compensation, as that is up tp your employment agreement and the state unemployment law.
I would not be surprised if labor or union agreements might have a significant effect here. That is why I am sending you to your benefits co-ordinator, so that he/she, armed with the literal wording of the tax law, can help you determine if you qualify for one of the four exceptions to be able to spend HSA money on health insurance premiums.
Thank you. Your answer is incredibly helpful. This is along the lines of what I thought, but you've given detail which will help a great deal.
HR did clarify previously that the coverage would not qualify as COBRA. That being said, I may try to appeal that as it appears that the unpaid leave would act as a "reduction in hours" COBRA qualifying event.