It's feasible but not necessarily sustainable. A lot depends on the type of work as well as how supportive an employer you have (if not self-employed).
From my own perspective I have a fantastically supportive employer and team behind me and if it wasn't for them I would probably have had to stop working a good couple of years ago.
As has been said, the problems come as the dementia and associated needs increase. In the early days my husband could occupy himself quite well and take care of his personal needs. He could even make himself a cuppa and something to eat if he wanted.
However, we are now five years into diagnosis and my husband is reliant on me for just about everything. I currently work three to four days per week. However, I am allowed to fit my hours in on weekends and evenings if I need to (great on days when hubby is ill, has appointments, attends memory groups or is greatly agitated to the point where it is impossible to work).
Some things have had to go such as live web meetings - I wasn't going to risk my husband's privacy being invaded or for my meetings to be inadvertently 'video bombed' by a wandering husband (I love my husband dearly but he isn't as cute as the two tots who recently gate-crashed their dad's live BBC interview from home and immediately became an internet sensation!)
Live web meetings aside, we still manage to get by with telephone conferences, instant message, email and social media.
But even with all the flexibility I am given, this past year has still been a struggle as a worker/carer - not least due to the lack of sleep I get now that my husband has regular restless nights.
Fortunately, the decision to give up/reduce working hours was taken out of my hands. Redundancies had to be made and, again thanks to my employer's tremendous support, I am about to embark on a job share of my post. I will work one day per week and my colleague will take the remaining hours - keeping us both in work.
It's the best outcome I could hope for. I keep my foot in the door, am able to keep my work skills up to date and will have the choice of working from home or working at the office (on a day when my husband is at his day centre).
Dreading the drop in income but I think we'll manage - the most important thing is that I'll be away from the stress of constant juggling, and hopefully will be able to enjoy more days out with my husband, from which we'll both benefit.