Is there theory that connects longevity, time-scale of environmental disturbance, and adaptation?
If the disturbance is short compared to a species' lifespan, then it's would be difficult for any adaptations to that disturbance to become fixed. Say an individual with a novel mutation is born during the disturbance that would impart some benefit under such conditions; since the species lifespan is much longer than that disturbance, by the time the individual reproduces, the disturbance will no longer be in effect and thus that allele will no longer be beneficial. In fact, this is seen in the thrifty phenotype in humans. When the mother experiences a period of duress during her pregnancy (say, the Dutch Hunger Winter of 1944), the fetus will undergo epigenetic changes that signal, in effect, that food is scarce and resources should be used sparingly. When those children grow up, they find themselves no longer under harsh conditions and this thrifty phenotype becomes a disadvantage, causing diabetes, obesity and so on.

If the disturbance is on the order of the lifespan of the species or slightly larger and especially if it is cyclic, polyphenism would be advantageous. This might also impart some resistance against long-term change, at least up to a certain point. For example, the butterfly Bycyclus anynana shows marked differences when born in the cool, dry season versus the warm, wet season: different body mass, different resting metabolic rate, different wing patterns and so on. This is controlled by hormonal switches in response primarily to temperature.

It seems that the best strategy in the face of long-term change would be gradual evolution due to progressive selection on traits that impart resistance to the disruption, at the cost of being vulnerable to future reversions in the conditions.

But of course, none of this can be "planned for" by the species. In the face of a new change in environmental conditions, be it gradual or sudden, the species can only work from its current genetic background. So whether there is a specific theory that deals with this (aside from the examples given above) is not clear. I would think that what we will see with strong-but-gradual climate change is a progressive loss of biodiversity (due to the inability to adapt in time) followed by rapid expansion to fill newly opened niches. To that end, I guess Gould's "Wonderful Life" would be appropriate to read. Any book on Evo Devo would lend insight into understanding how species might be able to rapidly adapt to a slowly changing environment, albeit in an indirect/abstract manner (i.e. "food for thought"); I like Sean B. Carroll's "Endless Forms Most Beautiful".