This BBC article, citing the food historian Caroline Yeldham, says
Breakfast as we know it didn't exist for large parts of history. The Romans didn't really eat it, usually consuming only one meal a day around noon, says food historian Caroline Yeldham. In fact, breakfast was actively frowned upon.
Quoting her directly, the article continues,
"They were obsessed with digestion and eating more than one meal was considered a form of gluttony."
This Smithsonian article more or less says the same thing and cites Yeldham in the BBC article. It's heading is
Mostly the Old And Ill Ate Breakfast Until the Rise of the Working Man
and the sub-heading is
Romans disdained the meal, few ate it in the Middle Ages, but most eat breakfast now
Wikipedia's article Ancient Roman Cuisine says
Traditionally, a breakfast called ientaculum1 was served at dawn.
and this article seems to agree, even citing details of the meal:
The usual time for their breakfast was early in the morning. The ientaculum, or breakfast, consisted of a buffet of flat, round loaves seasoned with salt were eaten. Rich ancient Romans, the Patricians would also have eggs, cheese, honey, milk and fruit included in these early meals
This article seems to fall somewhere in-between, saying "Romans were not big on breakfast" and that it was not a major meal.
From the conflicting information above, it seems that some Romans ate at least a 'smallish' breakfast. I would also surmise that farmers and soldiers probably ate some kind of breakfast, though there is also a reference to patricians.
Was there any particular class of Romans which didn't eat breakfast and considered it 'gluttony'?
Or are the somewhat conflicting accounts due to differences over time? (none of the sources are time-specific and Ancient Rome covers a period of over 1,000 years)
Did the later Romans, under the influence of Christianity, drop breakfast? I mention this because, due to the influence of Christianity, breakfast was not common in early medieval Europe.