The description of the Hex spell states (PHB, p. 251):
If the target drops to 0 hit points before this spell ends, you can use a bonus action on a subsequent turn of yours to curse a new creature.
The spell has a minimum duration of "Concentration, up to 1 hour" and possibly much more contingent upon spell slot level (8 or even 24 hours), so is there a limitation on what comprises a "subsequent turn"?
The way it is worded, it appears the Warlock could simply maintain concentration and keep moving the Hex around from one battle to the next (even maintaining it during a short rest with enough duration), so long as the previous target is reduced to 0 hp.
Best Answer
Yes, a warlock can keep the hex spell up outside of combat.
In-game, a turn is defined to have a duration of 6 seconds. When not in combat, you are not in initiative order, so turns are not structured rigorously. Nevertheless, your "turn" out of combat occurs whenever you have the opportunity to do something. As long as you have 6 seconds to spare, you can use your bonus action, and therefore you can redirect your hex.
As you noted, this is also implied by the extremely long durations that Hex can have. Nobody will ever be in a combat that lasts 8 hours (that's 4,800 turns!), so the only reason for the duration to be that long is to allow it to be maintained across multiple combats (or applicable social encounters) throughout an extended period. This is also mitigated by the Warlock's spell economy: they have very few slots to spend, so the requirement to spend a slot on Hex mitigates what could be perceived as an overpowering effect.