Also, a little secret I learned a week or two ago (maybe more). In the event you ever accidentally lose your Everstone - or even before it ever happens, just to be safe - get a Compound Eyes Butterfree, teach it Thief, and head to Reflection Cave. Every time you encounter a Roggenrola (run from anything else), use Thief on it. 60% of the time, it will be holding an Everstone (20% a Hard Stone, 20% nothing). Normally the odds are 50% and 5%, but Compound Eyes increases those. You can use this Butterfree as well at the Frost Cavern entrance by surfing for Poliwhirl (steal King's Rock), when in Cyllage City (or anywhere Luvdisc are found, Thief instead of catching for the Heart Scale), and even with Pikachu (I farmed Light Balls this way with a fainted Pikachu leading the party and Butterfree second, but note you don't get Compound Eyes activated this way; no problem since Pikachu would be super rare otherwise). Just remember to remove the item after you find you stole something; hands must be empty to steal another item!
If you run into a Roggenrola horde, Thief until you steal an item, then run away. No point fighting the entire horde.
(I've known the strategy for a while, but the Roggenrola is what I learned most recently.)