Green’s Dictionary of Slang

down adv.6

[lit. fallen down]

1. (US) collapsed, seriously ill.

[US]F.P. Dunne Mr Dooley Says 63: Th’ fam’ly are down with th’ whoopin’ cough.
[US]S. Morgan Homeboy 105: bitch down! [...] bitch be down big time.

2. (US) dead.

[US](con. 1958) R. Farina Been Down So Long (1972) 203: Heffalump down said the cable. One to an address in Harlem, the other for Beth Blacknesse.
[US]C. Cook Robbers (2001) 33: Agitated, frightened, brother cop down, stonecold dead.

In phrases

down as a dab [? a dead dab lying flat on a fishmonger’s slab]

very ill.

[UK] ‘’Arry on Equality’ in Punch 22 Feb. 85/1: Bin down as a dab with that dashed heppydemick, dear boy.