How did "ropey" come to mean "of poor quality"?
In ‘Chambers Slang Dictionary’, Jonathon Green suggests a derivation from ‘roup’, a form of catarrh and originally a disease of poultry. From the late 18th century it was used, according to Green, to describe an object or person that was ‘second-rate, inadequate, run-down, etc’ and came in the 1940s and 1950s to be applied to people who were unpopular. Any supposed connection with cords may thus open up a false trail.
The OED (second edition) says the adjective ropy (ropey) comes from rope and the first meaning given is:
1.a forming or developing viscid, glutinous, or slimy threads; sticky and stringy.
The words "threads" and "stringy" clear evoke rope. So far, so good. Then follow quite a long string of examples where the word is always used in reference to unpleasant things, e.g.:
1480 Caxton Trevisa’s Higden iii. xx, Lentulus spat and Þrewe ropy spotel in his face.
1697 Dryden Virg. Georg. iii. 759 Roapy Gore he from his Nostrils bleeds.
1831 Youatt Horse viii. 150 A considerable discharge of ropy fluid from the mouth.
And apparently the word was used in the figurative sense as early as the 18th century:
1768-74 Tucker Lt. Nat. (1834) II. 534 If there be any thing of..selfishness, or other passion intermingled, it is ropy and imperfect.
Ropy beer seems to be a concept that goes back a long way, and it is something that looks and tastes bad:
A thunder storm will sometimes case excellent beer to turn ropy; that is, to have an oily glutinous appearance, and a very unpleasant slimy feel in the mouth...
(Christian Gleaner and Domestic Magazine, Volume 3) 1826
From all these examples meaning 1.c. in the OED seem pretty logical (to me anyway):
c. fig. Bad, unsatisfactory, unreliable, unwell. slang and colloq.
Certain bacterial infections of beer result in viscous, glutinous strands as described in the OED quotation above, as well as spoiling the flavour. Beer suffering these effects is described as ropy (or ropey). It seems a short leap for "ropey" to then be used to describe anything of poor quality, with a particular connection to feeling unwell/hungover, although I have no evidence to back this up.
It seems fairly conclusive from the OED that modern use of the term began in the RAF in 1941. (The OED does produce a sole example dating from 1891 which they say no more than it 'may be an example' of this usage.) Since several of their examples relate to aircraft - 'a ropey old plane'- I am wondering if it may have something to do with aeroplanes held together with rope. We do talk metaphorically about things being held together with string and cellotape, but we don't speak of something being 'stringy', at least not in that sense. My guess is that 'ropey' referred originally to something patched up with rope. Having said that, there are no naval examples given, which is the service which traditionally uses ropes on a large scale. Please regard this answer as a 'stab in the dark'.