I caught the first James Lee Burke Dave Robicheaux novel and have stuck with him, the indestructible Clete, and the series of Dave's wives who rival Dr. Watson's, even though Dave goes through more constant existential angst than most armies going into battle. He was also an officer in Vietnam and dead members of his platoon used to visit him but they've faded away while Dave keeps going strong—other ghosts from his past and from the Civil War visit him regularly—with Dave and Clete recovering from multiple gunshot wounds as frequently and easily as some lesser detectives go through minor bouts with bumps on the head.
Because Burke's real-life daughter Alafair is now grown up and writing angst-filled mystery novels of her own, I have this deep fear that Dave Robicheaux's adopted daughter Alafair (also somewhat addicted to following gangster-killers into romance), will end up becoming the detective of the series.
Hieronymous ("Harry") Bosch also had his foot nailed to time's floor in the early novels by remembering when he was a tunnel rat in Vietnam. The gifted Michael Connelly reminds us often of Bosch's unspecified advancing age and imminent retirement, but one trial-balloon novel where Bosch retired became a sort of cold-case P.I. First-person narration of the novel (à la Spenser, Robicheaux, and the classic Hammett/Chandler books) was somewhat of a disaster, and Connelly had the good sense to send Bosch scurrying back to the L.A.P.D. and third-person narration. (The new stream-from-Amazon "Bosch" TV series may put Harry back a few decades when we get used to the actor's younger age.)
My favorite off-duty P.I. character of all time wasn't really a P.I.—it was John D. MacDonald's Travis McGee, a salvage expert who took cases to find lost things, usually people. His life on the Busted Flush houseboat parked at Slip F-18 at Fort Lauderdale's Bahia Mar yacht basin, a boat won by Travis in a poker game, approached Sherlock Holmes's 'downtime' as the richest and most believable private life of any working detective.
The friendly, suntanned giant named Travis had more philosophical speculations and social and gender judgments than any other fictional P.I.-type character I know, and it's these mostly 1960s-based lamentations about the social and ecological decline of the Florida coast that nail McGee in time. If MacDonald saw the stretch of Florida now, some 40 years after the writer's death, he might have had Travis sing hallelujahs about the cultural and natural pristine shape Florida was in then.
The Travis McGee novels continued from 1964's The Deep Blue Goodbye to 1985's The Lonely Silver Rain, which, perhaps by accident, had the perfect grace note for the series to end on. Though Travis's past military service didn't nail him to some advancing age, the series suffered irreversible changes: sidekick Meyer's boat the Maynard B. Keynes getting blown up, the Alabama Tiger (usually offstage but his parties always audible) dying suddenly of a heart attack and his endless 24-hour boat parties ending just as abruptly; a certain elegiac air filled the later Travis McGee novels.
No, Sherlock Holmes and his creator had it right. As improbable as it was that such a vital man as Sherlock would retire (to beekeeping!) in his forties, it was right that the "new" Sherlock Holmes tales printed after the turn of the century were usually "newly discovered case studies" from the 1890s. Holmes wasn't nailed down to time; he was a pivot upon which the 1880s and '90s turned.
The fog curls against the windowpanes. Hansom cabs rattle by in the fog, the sound of their horses' hooves muffled by the fog. No new client arrives. Dr. Watson disappears into writing up his case notes. Holmes is plucking randomly, irritatingly, at the strings of his violin. On the steps outside their door, both men hear the familiar swish and light footfall of Mrs. Hudson bringing up their afternoon tea. Perfection. Time stops there.
But I love all of the other noir, P.I. characters I've mentioned (and many more, of course.) And as long as it was the original writer giving us the glimpses of that character's life outside of the adventures, I was eager to peek. And to listen. And to hoard up facts about the character the way a squirrel hoards acorns. And to enjoy them all.