IMO the welfare implications of 'length of chase' is not as cut and dried as it first appears.
If I am chased for half an hour (the average fox hunt lasts under 31 minutes) through the woods by a predator that I can hear, my fear would be greater than being chased for 30 seconds, but my imagination would contribute a great deal to that fear. During a longer chase the imagination would be continually ratcheting up.
Humans have language, stories, films, imagination and the power of existential thought. We can think, "what if he catches me?", "what must it be like to die?", "I hope it won't hurt".
Theories of animal learning indicate that an animal learns from previous experience (e.g.Operant Conditioning) as opposed to 'what if' scenarios. If the animal has never been hunted before, or has been hunted and escaped, it has no reason to believe that it won't get away
this time.
Because we can't ask an animal how it feels - and heaven forbid that we fall into the trap of anthropomorphism
- we can look at behavioural indicators and scientific evidence of brain chemistry.
Behavioural Indicators
I have personally seen a fox sit down in the middle of a ploughed field and groom itself while the pack is closing in. To all appearances it did not look concerned, otherwise why choose that moment to attend to its fleas?
A friend of mine has seen a fox in similar circumstances initiate its own hunt (of voles or mice).
The foxes in both of these instances didn't act as if they were terrified - as a human would be, they acted as if the sound of the hunt was an annoyance that they could choose to move away from at their own pace. I believe that it is only when the hounds are
right there on the spot that the fox is/was let down in its assumption that it can get away.
The Burns enquiry concluded in the case of hares hunted by scent hounds that the hares often didn't even realise that they were being hunted.
It is natural for a wild animal to move away from the sound of disturbance. I don't think we should automatically read this as an animal being in fear of its life.
Brain Chemistry.
There have been some studies done on animals (not the fox as far as I'm aware), and man, to test the levels of adrenaline, endorphins and cortisol of hunted animal carcasses and soldiers during combat.
The Burns report mentions source material from reports by Bateson and Harris, Phelps, and by the Joint Universities Study on Deer Hunting. Bearing in mind that the evidence relates to deer, Burns concludes:
Although there are still substantial areas of disagreement, there is now a better understanding of the physiological changes which occur when a deer is hunted. Most scientists agree that deer are likely to suffer in the final stages of hunting. The available evidence does not enable us to resolve the disagreement about the point at which, during the hunt, the welfare of the deer becomes seriously compromised. There is also a lack of firm information about what happens to deer which escape, although the available research suggests that they are likely to recover.
So, although scientist of all shades of opinion agreed that in the
final stages of a hunt the animal's chemistry indicated that it was under stress, there was no unequivocal evidence that an animal which escaped prior to that stage showed "capture myopathy" or "emotional stress". Neither were these raised levels of cortisol seen in animals shot
during hunting but before the final stages.
However adrenaline
is released during the fight-or-flight response at the initial stages of a hunt, and endorphins produced shortly after. Endorphins are linked to the feeling of euphoria that the risk-seeking 'adrenaline junkies' are addicted to.
In man the levels of endorphins actually elevate rather than depress mood, as confirmed by the studies of soldiers during combat. Endorphins in man produce euphoria.
Obviously we can't ask animals how they feel to be hunted, but the brain chemistry indicates that their systems were flooded with endorphins, and it was only at the very end of the hunt that animals evidenced high levels of cortisol which fell outside the norm for sustained exercise (comparable levels to endurance horses and human athletes).
Some people may imagine that the animal would be "frightened out of its wits during a hunt". It may be convenient to attribute human emotions to an animal but the point that I'm making is that we don't
know.
We can base theories on scientific tests of brain chemistry, but those that have been done suggest the exact opposite, at least until the final stages of a hunt.
Personal observation also suggests the opposite.