I'm pretty sure they do run out.
I got caught on the surface north of Scotland one day, a DD came right at me out of the fog.
So I ordered crash dive and tried to evade.
It took a while but, after ca. 80 DC's he stopped dropping them on me.
He continued the search for several hours but around midnight lost contact (or gave up).
I think a better question would be: "does anybody know how many DC's are carried by the respective DD's and other escorts?"
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