As an addition to tofro's answer I only want to point out/ stress some hints from the comments:
If you want to omit repeated articles than you often (not always*) need the first and (always) omit the rest.
You just have to be aware which nouns are part of your list to have omitted articles.
In comparison the two examples:
Wir gedenken der Verwundeten, der Gefallenen und der Vermissten des Krieges.=>
Wir gedenken der Verwundeten, Gefallenen und Vermissten des Krieges.
Es war eine Zeit des Glücks, des Friedens und des fröhlichen Zusammenseins.=>
Es war eine Zeit des Glücks, Friedens und fröhlichen Zusammenseins.
As you might see:
des Kriegesis in genitive but not part of the list.
*As vectory points out, you can even have sentence constructions to omit all articles:
Eine Zeit voll Glück und Frieden. Im Gedenken an Verletzte, Gefallene und Vermisste des Krieges.
When to omit and when not?
In my opinion it depends on overall context. With the articles I can stress more the nouns, without it is more a "long concatenated list".
That is why I would prefer
an die Verletzten, ... because it is feels like a reverent moment speaking about it. In other cases they make the sentence longer and I guess in speaking I would more likely omit them while in writing put the articles there. Or maybe just thinking about the sentence let me put them in and not long thinking omits them. Good question.