I had an AE award refund of taxes take about 4 days to process, but had been told it could take 2-3 months. Also had an AMEX refund for a JAL ticket where they told me it could be up to 3 billing cycles, but it took 22 days (thankfully clearing 2 days before an automatic withdrawal of just under that amount!). And an AS reward cancellation where the refund took about 2 weeks. It's all over the board.