According to the printed rules, the Sky Stalker* archetype does not lose the Favored Terrain feature.
The Sky Stalker archetype on d20PFSRD does not exist in any of the books. Instead it was printed as "Sable Company Marine" in Inner Sea Combat (2014), and the corresponding entry on Archives of Nethys has the correct name. The text is otherwise the same; the archetype features do not mention losing the Favored Terrain feature. Thus the ranger doesn't lose it by taking this archetype.
Note: The table on d20PFSRD may be accounting for a 2010 Paizo blog post, which first introduced the Sable Company Marine. In this original version, the archetype did lose Favored Terrain. However, developer blogs are not the same as printed rulebooks, and the archetype is written differently in Inner Sea Combat, which was printed 4 years later. This has not been addressed by errata.
So we can assume that the Sky Stalker / Sable Company Marine does not lose Favored Terrain.