Well, this is going downhill fast.
To the original topic: My first reaction was "You can't sustain hex through a short rest," but after some thought I've changed my mind. The long duration of hex in higher-level slots strongly implies that it's meant to be sustainable through short rests.
Strongly agree. I can't imagine they weren't aware of the implication. At 8 hours or more, it is obviously going to intersect with short tests. My group saw that straight away, and it factors into how good those spells are. Ignoring the warlock and the bag of rats for a moment, let's look at the ranger or vengeance paladin, and Hunter's Mark. Works the same way, just without the bag of rats thing. Do folks really think they are meant to lose the higher level benefit of these spells when they take a short rest? If so, what would the point of the increased duration even be?
That being the case, I prefer to allow the PC to just cast the spell without a target. The bag of rats is one of those things that's amusing the first time, but quickly becomes annoying. Plus, while highly appropriate for the Fiend patron, it's less so for, say, the Archfey.
That is a good solution, IMO. elegant. For me, though, I think that an animal sacrifice fits the ArchFey just fine. It fits the "pact with an otherworldly being" flavor, in general, imo.
Side note, I'm pretty sure the rules would have to state somewhere that taking a short rest breaks concentration, in order for it to do so. The general rule is that you lose concentration under a specific set of circumstances, like taking damage and then failing a check, or being incapacitated. hanging out and having lunch isn't listed, and there is no specific rule stating that taking a short rest breaks concentration.
The other side of the issue is whether you can maintain concentration while taking a short rest, and actually gain the benefits of the short rest. But again, no general or specific rule speaks directly on this specific interaction, so we have to look to the general rules for resting, which are fairly clear. You have to spend an hour doing nothing strenuous. There is no indication anywhere in the rules that concentration is strenuous, and in fact, you can concentrate while doing just about anything, even being stabbed, if you make the check successfully.
So, I'd say it's pretty clear that, by RAW, you can keep concentration during a short rest.
I'd also say that it is absurd to think that concentration makes it impossible to take a short rest, when things like repairing armor, cooking and eating a meal, etc, don't.