Organisms who are unable to adapt to recurring or persistent change in the environment would most likely have difficulty surviving as individuals as well as on the species level. That being said, every species and environment is difficult, so survival strategies may differ.
Organisms who cannot adapt to recurring or persistent environmental change are likely to experience a high degree of physical stress due to lack of food and water, problems with thermal regulation, or access to shelter. Such stress may induce an increase or decrease in attempts to procreate depending on that organism's typical behaviors, but females who are under high stress are not likely to produce viable offspring. Since the problem is with adaptation, any viable offspring are even less likely than their parents to successfully reproduce in the wake of recurring or persistent change.
Let's consider a very real problem threatening many organisms today: global climate change. We are in a period of global warming caused by human activity that is resulting in an increase in global temperatures that is far more rapid than anything ever experienced before. Evolution naturally occurs over many thousands and millions of years of gradual change in response to environmental pressures. A very slow change in temperature--say, one degree warmer or cooler every thousand years--would give species plenty of time to adapt to this change. The rate at which global warming is currently occurring is too fast for a significant number of organisms to keep up, and those which can't adapt are likely to go extinct. Species like the Golden Toad (Bufo periglenes) have already gone extinct because they cannot adapt rapidly enough to survive in a warmer climate. Many more species are endangered or threatened by the prospect of global warming, either directly due to temperature, or indirectly through loss of habitat and food sources.