Apparently, this question is breaking the internet:
It’s funny 'cause it’s true!
I answered “weekly” but it probably depends, sometimes it’s more like monthly and other times daily.
It depends on what you mean by “think about”. If you’re asking, when do I spend a good amount of time thinking about something related to Rome? Well, probably closer to monthly - I like my history podcasts, blogs, etc and Rome comes up a lot.
If you mean when the Roman Empire pops into my head even for a moment - daily, for sure. References to Rome are absolutely ubiquitous in our culture, and because I’m a history fan I tend to catch them long enough yo think “heh, Rome”.
But how often do women think about the Kushan Empire? I think that’s what we all really want to know.
Joining the club, here. There are times that something brings it to mind but it’s not an absolutely regular thing. There may be some article that catches my eye and the algorithm then pounces on it and I can’t avoid it for weeks.
Babale put it better, there is a difference between “think, as in really think” about the Roman Empire and just almost unconsciously have the fact of Rome being a referent for a lot of things in Western Civ make it inevitable to have it somewhere there in the background when you think about some subject.
As Isaac Asimov once wrote:
Apropos quote:
Take an Empire that was Roman and you’ll find it is at home in all the starry Milky Way.
If you can reach Kevin Bacon from any actor in six steps, you can probably reach The Roman Empire from any concept in three or four.
I guess if we cast our net wide enough (ie, thinking of a Latin term @Kent_Clark mentioned; thinking about Roman inspired architecture or art without thinking about the Empire itself; etc) then “every seven seconds” may not be far off.
Occasionally, when I see a Trojan advert.
It almost never enters my mind, unless it comes up in conversation. And it almost never comes up in conversation.
The inadvertent wisdom of Yogi Berra, on the other hand? Now that is relevant almost daily. You observe a lot just by watching, you know.
To add, I think about the Roman Republic too.
I follow the acoup.blog site by Bret Devereaux, a historian of classical antiquity so his weekly posts are frequently about, or reference, the Roman republic/empire. I put monthly on average.
Even had I not just found out this was about wives asking their husbands how they thought about the Roman Empire I would’ve answered “Every day”. So I am not surprised at those answers in the video clip. The OP left out that context.
Context isn’t important here. And why would you answer differently for your wife?
Because you don’t want her to get jealous?
Because my wife doesn’t ask me things like that out of the blue so I’d assume there was some kind of game going on. It’s witty and clever interplay to us even if not to anyone else.
I need a “Erm, what?” choice.
Probably the only time in my life that anything remotely like the Roman Empire was something I actually thought about (outside of maybe history class) was when a friend and I were staying at the Hedonism resort in Jamaica, and it was toga night! 
Romanes eunt domus
Maybe not actually monthly, but several times a year at least. Not sparked by movies, but by thinking about archaeological finds, or their impact on the modern world.
After listening to The View segment, I’m positive the men are mixing up the Roman Empire with Sparta and the movie 300. Or maybe remembering the nude scenes in the tv shows Spartacus and Rome.