I accrue to AAdvantage
and I've kept a record of my accruals this year:
5 QF flights took between 2 and 4 days to post
6 QR flights took between 1 and 7 days to post
1 BA flight took 3 days to post
5 AA flights took between 1 and 3 days to post
2 UL flights took 5 and 6 days to post
1 CX flight took 6 days to post
All flights accrued without my having to request them