Ridership never recovered on the south side, but it had already been declining. The area around the South Elevated and both of the branches (Englewood and Jackson Park) had been depopulating consistently for 50 years, following desegregation when African-Americans were finally allowed to disperse from the south side ghettos that were incidentally concetrated along the south side elevated.
(density within 1/2 mile of L)
Ridership on the south elevated was strong-ish (about 3 times current levels) as recently as 1990. Since that time, the mainline (north of 59th junction) has recovered a decent chunk of its ridership and is still on a modest upward trajectory, currently at 60% of its 1990 ridership level. However, the 63rd branches have simply seen their ridership evaporate, which was a process that started in 1991 and continued through the line reconstruction. Ridership on each of the branches has stabilized since 1998... but at only 30% of their previous ridership.
Ridership recovered after closure on the Lake Street branch by about Year 2000. Interestingly, Lake Street depopulated too - but Lake Street ridership has been growing steadily since the reopening in 1996. Either way, the success on Lake surely implies that the reason for south side issues is much deeper than an 18-month line closure.
EDIT: it's worth noting, in the above chart, that I didn't "control" for the growth of the Milwaukee/O'Hare branch over the time period. Of course between 1960 and 1970 the line was extended from Logan Square to Jefferson Park, and then between 1980 and 1990 the line was extended to O'Hare, so to a large extent the decrease in density on this branch was only because the line was being extended into lower-density neighborhoods rather than depopulation of existing neighborhoods, as occurred around all the other branches except those on the North Side, which have actually been getting denser.