“He’s refusing because he can’t manage the logistics, and he’s too proud to let us help him,” I said. But it was a pointless debate, and we both knew it. The real problem is not my father’s level of functionality; it’s the lack of available Medicaid beds and the absurdly high cost of any meaningful alternative. For example, there’s a lovely assisted-living facility just two miles from my parents’ apartment. But it costs $8,000 a month, on average, and does not accept my father’s insurance .

Like approximately four million other American families right now, my mother and siblings and I are plugging this gaping hole in our nation’s safety net as best we can. My sister has become an expert at talking my father through his rages — a common feature of dementia — and makes daily, herculean efforts to negotiate with him about basic hygiene, what he eats and how much he smokes. My nieces bring meals over as often as possible. And my mother prays and counts blessings — even on the worst days, when she has to lock herself in the bathroom to escape his mood swings. I am currently pleading with several entities for a visiting nurse, at least. I worry about my mom’s ability to manage my father’s medications, and I think several times a day about how serious an error in that department could be.

In the midst of all this, we are constantly gauging how much our father is still “here” with us. Sometimes I interview him when I visit, asking him what he remembers about his life and mine. But most of my efforts are more clandestine. We play Scrabble, and I search for clues in the words he makes. (He’s still quite good at the game, though he’s a bit of a cheater.) Or we watch old movies, and I study his face for glimmers of recognition. Sometimes I imagine him hacking his way through the dense plaques that are taking over his brain the way an explorer hacks through virgin jungle — his epic quest is to be present with us in the living room.

My father has always had a sense of the epic. When I was little, he and my mother regaled me with stories of the adventures they had, across Europe and South America, before I was born. As an adult, I have made it a tradition to reciprocate by reporting back to them from every country I visit. In October, I called them from Barcelona to describe the flamenco dancers and Gaudí buildings. My father started crying when he heard my voice, and my mother and I tripped over each other in a rush to calm and comfort him.

“Stop crying” I heard her say in the background. “Everything is O.K.”

“It’s O.K., Baba,” I told him. “Cry if you need to .”

“What’s wrong?” we asked in unison.

“I miss you,” he said. “I miss you all so much.”

We miss him, too. We would like to savor our time with him, but we’re often consumed by the work of keeping him safe. There are nine of us — one wife, three adult children and their spouses, two grandchildren — and just one of him. And still, we scramble. Last week, he disappeared off the front porch without a word, sending my younger niece into a tear-streaked panic.

“He was literally right here two minutes ago,” she told my brother over the phone. She had searched the yard and the street, and checked with the neighbors on either side, all to no avail. It was getting dark, the temperature was dropping, and my parents’ neighborhood is not totally safe at night. They were debating whether to call the police when my father emerged from a stranger’s car and ambled onto the porch with a fresh pack of cigarettes. (We probably owe somebody 10 bucks for those.)