The apiary at the Lakeview Manor does not refill with bees or honey. When I first built it, I took all of the bees and honeycombs away on accident. I put two of the bees back thinking they would multiply, but after waiting several months in-game, nothing has happened. Is there a way to make the bees breed and create more honeycombs? I would like to use them for potions.
The Apiary respawns every 10 in-game days, provided you are not near the house.
Simply go away (unload the cell by being in Whiterun or similar -- once you see the loading screen, you're good) and wait about 10 days and come back. The Apiary and everything else that should respawn will respawn.
If you are on PC, I highly recommend that you get the unofficial patches for your game:
- Unofficial Skyrim Patch: Get this no matter what DLC you have.
- Unofficial Hearthfire Patch: Will fix a ton of Hearthfire bugs. Get it only if you have the Hearthfire DLC.
- Unofficial Dawnguard Patch: Dawnguard bugs? Whassat? Get it only if you have the Dawnguard DLC.
- Unofficial Dragonborn Patch: Fixes a lot of Dragonborn stuff. Get it only if you have the Dragonborn DLC.