I’ve got a bit more info now. Green’s Dictionary of Slang has an entry:
[? link to dial. dobber, a ‘wonder’]
(US) spirit, morale.
1913 [US] Eve. Times (Grand Forks, ND) 6 Jan. 4/4: In the majority of cases two or three returns from the big show serve to get a recruit’s angora and his ‘dauber’ goes down.
1925 [US] R. Lardner ‘Women’ in Coll. Short Stories (1941) 154: The boys were depressed. In their own language, their dauber was down.
1947 [US] C. Willingham End as a Man (1952) 158: Don’t get your dauber up, let me explain.
1953 [US] Randolph & Wilson Down in the Holler 258: keep your dobbers up: phr. To keep up one’s courage.
1967 [US] (con. 1920s) J. Thompson South of Heaven (1994) 117: He [...] told me to keep my dauber up.
I don’t know where Green gets the reference to dobber, a wonder. But according to DARE, a dobber is also a bobber or float on a fishing line in New York/New Jersey dialect. Quotes go back to Washington Irving. (Not of the phrase, just of dobber being used to refer to a float.) The use of a word for a fishing float to refer to unsinkable morale makes a kind of sense.
One of the old Yuku threads is here. Evidently there was more than one.