Does anyone know if learning a second language diminishes with age?
Yes. By around 35, there's a marked increase in difficulty.
I mean, is it unrealistic for someone in their 60's or 70's to think they could learn a second language?
Depends what you mean by "learn". If you mean get a job as a translator, it isn't going to happen. You won't get to that level of fluency, where you can instantly translate between your native tongue and the newly acquired language.* However, that doesn't mean you can't become reasonably proficient, being able to read a book and comprehend it, or learn "tourist level" conversations.
It's not likely to be as easy as it was when you were 20, or 40.
Not fluent, but 'get-by-well' with what they know?
That's realistic.
Around 5 years ago, at age 50, I decided I wanted to get past very basic French to somewhat more passable. It worked. I got to the point where I successfully made it through two French novels, without reading the English. (They were "Tour de Monde en Quatre-vingt Jours", by Jules Verne, and "L'annee de l'Isle", a modern "young adult" work, whose author I don't remember. I also started on "Notre Dame de Paris", known in English as "The Hunchback of Notre Dame". I found that level much more difficult. Victor Hugo used a lot more sophisticated vocabulary than Jules Verne.).
I also taught myself a bit of Hebrew, to where I was reading children's books passably, with no prior knowledge of the language. I found, though, that after taking a year off and picking it up again, I had lost almost all the knowledge of it. That's a common complaint among older learners. I remember more German, which I studied briefly when I was 20, than Hebrew, which I studied five years ago.
I used Hebrew vocabulary cards for vocab building. I didn't need that much in French, because I had some prior knowledge. After that I tried to read stories in the native tongue. I read "L'annee de l'Isle" as a Kindle edition, and when I didn't know a word or phrase, I dropped the sentence into google translate. It is quite good these days.
A program I haven't used much, but that looks good to me for vocabulary, is Anki, a free flash-card style program, with an awful lot of community produced vocabulary decks.