I had to take a break from shooting my 1958 Bear Kodiak to respond to this. Just kidding – it was my 1968 Bear Grizzly. Or maybe it was the custom selfbow made for my dad … in 1943.
As noted above, if the bow is in good condition, there is no reason not to shoot it. The bows from the ’50s, ’60s and ’70s will probably go on killing game long after we Boomers have passed from the scene.
As for the strung/unstrung question, you’ll hear all sorts of opinions both ways, some occasionally taking pains to differentiate between longbows and recurves, selfbows and all other bows, etc., etc.
I leave my fiberglass-laminate recurves strung. Until I get nervous about the weeks that have passed. Then I dither long enough to remember that the whole reason I have them is to shoot them, and it’s handier to keep them strung and I do more shooting that way. (Makes no sense, but there it is.) I do leave my selfbows unstrung. When the snow gets too deep in the winter for stumping, I unstring all of them. At least for a week or so …