[Update: Adobe Engineering has declared this to be working as intended; if you want this ordering to persist, a workaround like that provided below will need to be implemented.]
We discovered what looks like an oversight/bug in AEM 6.2 Assets collections (we have not investigated if this is a problem in earlier versions.) When you reorder the assets in a collection in the UI, the underlying order does not actually change (if you refresh the collection view the order goes back to what it was before). In other words, the ordering of a collection in AEM 6.2 the order is set at creation time, and you cannot make persistent modifications to it.
A customer’s project requirements included the ability for authors to change the order of assets in a collection, so we made a quick and dirty fix for this issue. Here is a link to download the code we created to get around the problem. It’s not our preferred solution, but it gets the job done. We have submitted a ticket to Daycare which has been escalated to the Engineering team and assigned ticket ID CQ-94530; if you are interested in this issue, you can use this ticket ID to watch Package Share and the Release Notes for an official patch from Adobe for this issue.