The term "mainframe" was also used for the part of microcomputer cases that held the expansion cards, but they weren't referring to the computer itself.
It seems to come from microcomputer hardware and accessory companies trying to throw the word "mainframe" into their ads somehow and make their stuff seem more important.
While the term "mainframe" was common in advertisements, it was also used in the article text of magazines.
For example:
"MERLIN (trademark of MiniTerm Associates) is a new concept in peripherals modules for mainframe microcomputer systems." (Merlin was a dumb terminal for IMSAI and Altair desktop comptuers) - Byte Magazine, November 1976, page 64
I only knew of "mainframe" used in the fashion that drfuchs described. Out of curiosity, I did a search of archive.org looking for uses which match your description. Here are two of the matches:
"Model 706 mainframe can accomodate 10 scanner plug-in cards. ... Before operating the Model 706, the appropriate scanner cards must be installed into the mainframe. Each scanner card (up to 10 cards per the Model 706 malnframe) is Installed in the appropriate vertical slot In the rear panel of the Model 706. Refer to Figure 2-1 for an overall picture of scanner card installation." https://archive.org/details/keithley_KEI_706_Instruction/pag...
"Peripheral cards, capable of handling words as large as 32 bits, perform operations normally requiring expensive computer mainframe expansion — display control, multiple capstan tape control and the like." https://archive.org/details/TNM_832_Data_Interface_-_ECG_Dat...
However, that isn't what reaperducer referred to when saying "the term “mainframe” seems to have become exclusive to big iron only in the mid 1980’s."
> What is, a minicomputer? Unfortunately, the term minicomputer is used by many people with many different meanings. For the purpose of this paper, we shall characterize a minicomputer by the following two criteria.
> (1) Physical size . Typically, the main components of a minicomputer (its CPU and main memory) are closer to the size of an electric typewriter than, say, a washing machine. (Not counting the power supply and racket, the CPU and memory may fit on a single printed circuit board!)
> (2) Cost . Typically, the main components of a minicomputer (its CPU and main memory) can be purchased for less than $10,000 - in some cases for less than $1,000.
This is clearly more like a machine we would call a desktop - how many people have washing machine-sized computers on their desktop?
A 1975 report titled "Use of Minicomputer Facilities for Higher Education Instruction" helps identify that 'minicomputer' was a new computer category starting in the late 1960s, quoting https://archive.org/details/ERIC_ED112763/page/n3 :
> Although each of the methods offered a level of computing suitable for some instructional use a belief was expressed in 1969 that the new "minicomputers" might be able to provide instructional computing support that even the smallest colleges could afford.
It seems to come from microcomputer hardware and accessory companies trying to throw the word "mainframe" into their ads somehow and make their stuff seem more important.