What we're wondering about it is when we should retreat the wood.
The basic rule is, when it looks like it needs it.
After a certain period the wood will have started to look a little dry, pale and/or slightly greyish, that's approximately the stage you should apply a fresh coat of oil. If the wood has gone distinctly grey you've waited too long :-) This isn't fatal by any means so there's no need to panic if you skip the recoating one summer, it's mostly a cosmetic issue.
Something to note, you should find that subsequent coats aren't needed as frequently as the first recoat. This is because the slightly degraded surface of the wood is more absorbent so later applications hold more oil, which then lasts better than the initial treatment.
Are there rough estimates for when (vertically placed) outdoors wood should be retreated?
There are guidelines given for different climates but they are only rough and you should be guided by the wood itself — your climate and local conditions, the wood in question, even the specific oil you're using*, all play a part in how long the treatment lasts.
You'll find that any localised areas that are protected, e.g. by the overhang of a roof, will have degraded much less than the wood below which is more exposed so won't need recoating as frequently. You may also find that anywhere rainwater can splash back onto the walls will degrade fastest, this normally occurs at the bottom of any wooden wall or door near the ground. With a beehive it may only be noticeable at the front if there's a ledge provided for the bees to land on.
When it comes time to apply fresh oil, don't think "one coat good, two coats better", just apply one coat. It doesn't matter how you apply it, by brush, roller or rag, after a short wait (half an hour or so) wipe any excess from the surface where it hasn't been absorbed.
Note: oil finishes are most suited to dry climates
Straight oil finishes perform less well in damp climates, especially those subject to long periods of rainy weather. Woods treated with oil that stay damp for extended periods are prone to attack by moulds (mildew/fungus) and a dark discolouration can occur, which at worst can turn the wood nearly black. This problem can really only be prevented by incorporating some anti-fungal agent into the oil.
Commercial water-repelling penetrating finishes already incorporate a fungicide so are preferable to a raw oil in any wetter setting. However, many also contain a high proportion of solvent which may be a problem for use on a beehive with a resident population of bees. If the hives can be refinished when not currently inhabited this solvent is not a concern however as every trace will evaporate.
*Linseed oil is a natural product and can and does vary. Even different batches from the same producer should be expected to vary slightly.