Quite a few owners on the Fiat 500e Facebook group have reported this (after the battery was replaced). One FIAT dealership has suggested that the remote is sensitive to battery manufacturer, and they recommended use of Panasonic or Energiser. It may not be as daft as it sounds; some batteries have a slightly different profile to others so do not make as good contact with the key fob connectors as they should. Might be worth a try...