Why the Greenbelt dries up (and comes back)
Barton Creek loses water as it flows through the Edwards Aquifer recharge zone.
Barton Creek is intermittent: it's dry most days of most years. That's not necessarily a drought symptom, it is normal for the creek.
It's also a losing stream. Below the Hill of Life the creek crosses the recharge zone of the Edwards Aquifer, where the limestone karst under the creekbed is full of cracks and conduits. Water soaks into the rock as it flows downstream, which is why the upstream gauges can read healthy flow while Loop 360 reads near zero. The swimming holes get what's left after the aquifer takes its share.
That's why the order of the swimming holes matters. Hill of Life sits above the biggest losses and holds water the longest; Sculpture Falls and Twin Falls come next. Gus Fruh and Campbell's Hole sit farthest down the recharge zone and are usually dry: they hold water for a stretch right after very heavy, extended rain, and can go years between fills. Barking Springs is the exception, fed by the spring rather than the creek.
After a good rain the creek can go from flood to dry in days to weeks. The flow decays in a predictable curve: steep at first, then slower, as the watershed drains and the aquifer takes its share. That decay is why the real question is always about timing: "It rained Tuesday...is there still water Saturday?" Usually yes, if the rain was significant. Ideal conditions tend to arrive 3 - 7 days after rain, when the bacteria flush has cleared but the flow is still in the 15 - 50 cfs range.
Where does the "lost" water go? A lot of it comes back out at Barton Springs, the aquifer's main outlet. This is why Barton Springs flows year-round (typically 50 - 90 cfs) even when the creek above is dry.