Pokemon Global Link or PGL is already down, so any Functions for Spending Pokémiles and receiving items, or Ranked battles is now down.
PSS and GTS are relatively lightweight on the server compared to PGL, but will eventually be discontinued, most likely when all Gen 6 online funtions will be discontinued. I should point out that since Pokémon is a "evergreen" title that this functionality will most likely be stopped when the 3DS online support is removed. There is No indication when this could happen, nor I think it will being even considered for at least a year. (We assume that Nintendo had little say in removing the DS and Wii support due to Gamespy servers also being cut at the same time.)
AS for offline support. Trading will still work, as long as both games are on the same patch. Local Battles, and o-Power sharing is still possible, as well as all Local functions that work today.