We discussed the proper spelling of this name on APBO the other day, so I
figured I'd ask Julian Shaw what he thought. Here's his response:

Thank you for your e-mail query.
The plant in question was named by Hooker in Curtis's Botanical Magazine
vol. 54: t. 2748 in 1827, as Zygopetalum mackaii. This spelling is followed
in several botanical works as you have indicated.

A number of other works use the spelling mackayi, including;
Pabst, Orchidaceae Brazilienses 2: 283, #1745 (1977),
Pridgeon, Illust. Encyc. Orchids 290 (1992).
Warren & Miller, Orchids of the high mountain rainforest... SE Brazil, 133,
#1745 (1994). McQueen, Orchids of Brazil 192 (1993)

The ICBN 60.1 states that 'The original spelling of a name or epithet is to
be retained, except for the correction of typographical or orthographical
errors and the standardizations imposed by ... Art. 60.11.'
And Art. 60.11 tells us to look at Rec. 60.C.1., where under (a) we can find
the example gray-i for Gray.
From this I would infer that mackaii, should be corrected to mackayi, as it
is formed from the name Mackay.
In the Orchid Hybrid Register, we currently treat mackaii as a synonym of
mackayi. However, I think it would be wise to seek a second opinion on this,
so I will copy this e-mail to my colleague Alan Leslie who has greater
experience in these sort of questions.

Best regards

Julian Shaw
RHS Orchid Registrar