I believe you have to be displaying a collection or a single folder to re-order photos
Could you possibly zip up your Lightroom catalog .lrcat file/folder, put it on dropbox or similar and PM me the location? We have not been able to duplicate this in house.
Some observations that might help others.
The collection I was trying to reorder has a filter for Picked photos enabled. It seems if I don't have the filter I can re-order but if I do, I can't?
Also, if I try to reorder with a filter based on star ratings only (where all picked photos are also 5 stars), they reorder fine.
These photos were part edited (and pick flag applied) in Lightroom mobile on iPad (latest version), part in Lightroom 5.5 desktop. This collection was created after I upgraded from 5.4.