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.