I've personally seen this, but it's never been reliably reproduced in-house.
Workaround:
1. Add the raster to ArcMap
2. Set the data frame's coordinate system to the target coordinate system (data frame properties, coordinate system tab)
3. Set the appropriate geographic/datum transformation (same tab, transformations button)
4. Right-click the raster layer in the table of contents and on the context menu, select data, export data.
5. In the export data tool, select the data frame's coordinate system.
Melita