I think that the notion of 24/7 D/s has something to do with continuity and consistency.
This is not to say that one has to be in "full metal jacket" at all times. Gardening in a latex corset (while stylish) is not terribly practical. Telling a cop who has pulled you over that he is a dirty little boy that needs a good spanking (while also stylish) may have unwanted results. Refusing to cash a cheque because the ingrates have neglected to make it out to LADY Nichola is taking a point of principle too far.
And even if one did stick doggedly to D/s conduct throughout the day - over time, it would make for a rather featureless way of life.
The answer to the question of how to live an authentic 24/7 bdsm existence lies, as others have suggested, in how one conducts oneself during the off-duty periods.
Is it easy to live with a slave who is beaten in the morning; works as a leader during the day; receives an award for her professional achievements in the evening ... and then, when she comes home, has her food set on the floor by a cage?
Short answer: No, it's not easy. And whether you live under the same roof or not, the central challenge is continuity. How do you shift from areas of your life which may require that you adopt vastly different roles... and yet live authentically as a slave.
The strategy that virtually everyone adopts is to compartmentalize these areas to some degree i.e. "Mom Mode", "Boss Mode", etc.
In a fully textured life, it is only reasonable to expect that these different modes of existence compete for time and psychic energy. Where things seem to go awry is when the competing demands squeeze out the time and energy for "Mistress Mode". In my experience, this is a common pitfall of the 24/7 relationship.
It is seductive, and indeed seemingly logical, to think of one's time as a Mistress as a separate mode of existence. In my early days, the strain of being "on" all the time was awful. To operate at that level of intensity is a recipe for burn-out. And so, quite logically, I tried to compartmentalize my on-duty time. There's nothing wrong with the strategy - we all "kick it up a notch" as the situation demands. However, taken to an extreme, the psychic whiplash that comes from turning the switch on and off is just as impractical.
That may be a little abstract, so by way of an example: Negotiating with my ex requires a hell of a lot of diplomacy. There's no place in those exchanges for an imperious soul like myself. (One of many reasons we are still not together) - But shifting from "Mistress Mode" to "Negotiating Mom Mode" and back again is tricky. Afterwards, it took a while to sort out whether I was a "Diplomatic Mistress" or a "Mominatrix"
Ultimately, I've arrived at a happier medium. With or without a live-in slave, I'm pretty consistent in how I live. My belief system (of which D/s is an important part) doesn't do flip-flops based on who I am talking to. The fact that I'm a Dominatrix provides a steady beat that underscores my life - and yet, paradoxically, it doesn't dominate my life.
The "idea" of 24/7 is not one idea, but many. It ranges from the Roissy fantasy to the live-in reality. In my personal travels through some of those 24/7 lifestyles, I've come to this conclusion: That the toughest and most rewarding 24/7 challenge - is how to be Myself.
Respectfully,
Lady Nichola