Yes 24 hours seems to be the limit, and I arrange my long flights carefully to take that into account when using SYS. Last week or so flying MEL-LAX-SEA-LAX-ORD-DUS the agent at SEA point blank refused to issue me the First boarding passes SEA-LAX-ORD-DUS as "I'd had my stopover in Seattle".
I very politely agreed I had stopped in Seattle, had taken an afternoon tour, then had drinks and dinner for 5 hours with a bunch of FT'ers and then had a nice restful sleep at the Doubletree,
but I had not in fact made a legal "Stopover" as I'd arrived only 21 hours earlier.
This cut no ice with her, so she phoned the It'l rate desk to find out how much to charge me for the SEA-LAX leg she said was illegal, and to "have clarified to me" the stopover rule. Interesting to watch her face as they explained it as I stood there. btw she then "waived" the illegal return leg to LAX.
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Glen ~