I have letters of recommendation, which I have publicly published (online).
I don't bother to keep track of whether each of the authors behind these letters continues to breathe.
If I found out that somebody has passed away, do you think I ought to go into my collection of published material and delete the content? The person's life has been snubbed away from the planet. You think I should go remove a positive thing that provides some ongoing evidence of this person's activity?
The point of these rhetorical questions is point out some of the reasoning to my opinion, which is obviously that it's fine to use the letter. If I were on my death bed with a week to live, but I knew I could help someone by writing a letter of recommendation, and if I bothered to write that letter, I wouldn't want them to tear up the letter into pieces in a couple of weeks just because I will have left my death bed by that point.