Finding precise studies seems to be hard, but I think we might be dealing with two factors: psychological and physiological.
On a psychological level, there is habit formation. Taking an extract from Wikipedia:
Habit formation is the process by which a behaviour, through regular repetition, becomes automatic or habitual. This is modelled as an increase in automaticity with number of repetitions up to an asymptote. This process of habit formation can be slow. Lally et al. (2010) found the average time for participants to reach the asymptote of automaticity was 66 days with a range of 18–254 days.
As the habit is forming, it can be analysed in three parts: the cue, the behavior, and the reward. The cue is the thing that causes the habit to come about, the trigger of the habitual behaviour. This could be anything that one's mind associates with that habit and one will automatically let a habit come to the surface. The behavior is the actual habit that one exhibits, and the reward, a positive feeling, therefore continues the "habit loop". A habit may initially be triggered by a goal, but over time that goal becomes less necessary and the habit becomes more automatic.
A day without running after consecutive days with running would be a break in the habit loop. Even if your habit is stated in your mind as "go running 5 times a week", that's what you believe the habit to be on a cognitive level, but subconsciously you've been conditioned to do this daily. So as a day passes without running the loop is broken and the impulse towards activity is lessened. The longer you wait, the further you are on the drop-off of the habit formation curve towards automaticity and it will once again take an act of willpower to start again. But upon successfully doing so you'll quickly move towards the previous level again; if you didn't wait too long you'll still be way better off than starting from scratch, and the downtime will in retrospect seem like a little hickup in what is otherwise a well-established habit. I think this might have some effect on that "wake-up" feeling you get when you go for a run when the lethargy is setting in. The positive effect on mood from re-establishing the habit loop would definitely have an uplifting effect. I know for one that if I spend a whole day lazing about inside watching YouTube, or spend the day going to the park, sitting in the sun and reading, the latter will leave me in a better mood and feeling more fullfilled and awake, despite both arguably having been "unproductive" leisure time.
In your case that doesn't seem to cover the whole story, though, since you mention this is specific to running and in other activities like cycling the time off actually contributes to recovery and a new-found readiness to take up the activity again. So we'd need to dig into the physiological aspects.
One possibility is that it is in fact a function of recovery. Namely, with the cycling you might be accumulating fatigue to the point where rest is needed after five consecutive days or you'll start seeing a negative return on investment (overtraining). Whereas with the running perhaps the applied volume and intensity is of a level you are already accustomed to, so without increasing these parameters recovery isn't as big a factor anymore and the habit formation becomes much more important.
This article on Wikipedia investigates the neurobiological effects of exercise: https://en.wikipedia.org/wiki/Neurobiological_effects_of_physical_exercise
Of particular interest is the section "Psychological stress and cortisol".
The "stress hormone", cortisol, is a glucocorticoid that binds to glucocorticoid receptors. Psychological stress induces the release of cortisol from the adrenal gland by activating the hypothalamic–pituitary–adrenal axis (HPA axis). Short-term increases in cortisol levels are associated with adaptive cognitive improvements, such as enhanced inhibitory control; however, excessively high exposure or prolonged exposure to high levels of cortisol causes impairments in cognitive control and has neurotoxic effects in the human brain. For example, chronic psychological stress decreases BDNF expression which has detrimental effects on hippocampal volume and can lead to depression.
There might be a difference between the cortisol release for running and cycling, possibly specific to your case. Are you more accustomed to running than cycling? Perhaps cycling causes a cumulative overload whereas running no longer does this for you.
Then there is the famous "runner's high". A prolonged bout of exercise (and I'd say running 8 miles might fit the bill) can result in feelings of elation due to the release of what is known as "euphoriants", which are in fact addictive drugs. Getting these on multiple consecutive days and then denying yourself them for a few days would very much lead into withdrawal symptoms. An example of such a substance playing a role in runner's high is beta-endorphin, an analgesic which has a (substantially) higher potency than morphine.
Is this specific to running, or some sports but not including cycling? A search around online yields some anecdotal evidence from cyclists that they too can experience this same feeling of euphoria and get "in the zone". But I'd hazard a guess that given the nature of cycling versus running (relative intensity, distance, possibility of letting momentum carry you for a while or downhill) you might need longer cycling workouts compared to running to produce the same effects.
My best guesses would be that you are perhaps more accustomed to running and training specificity can have a profound effect on the produced results, or perhaps being our natural means of displacement (as opposed to cycling), running is more effective at resulting in the release of the euphoriants. But both are pure conjecture on my part.
If anyone would find some specific studies regarding this it'd be very interesting. I'm coming up empty-handed without taking more time to dig through archives with the right keywords.