Most likely cognitive science and psychology fields will come together into one field of study, but only with technical improvements to be made. This trend has already begun, with more psychology departments conducting experiments that involve neuroimaging or EEG.
Cognitive science, while attempting to be a scientific field with empirical methods, has its theoretical backgrounds in psychology (such as attention, working-memory, consciousness, and so on). This provides a limited credibility to the current findings of cognitive science. We only know certain areas are activated during a task, but vague localization of brain area to a task is not enough for the understanding of brain mechanisms that is desired for practical applications. Only when experimental methods become higher resolution (enough to fully explain brain activities and behaviors with activations of certain neurons) will cognitive science become a full-fledged science.
On the other hand, psychology theories have been based on observations of behaviors and assumptions made by psychologists. With more concrete information from cognitive science, psychologists would be able to update their theories that are better backed by experimental evidence.
For replication crisis, well it comes from a lack of emphasis on replication studies by the research funding system in place as well as a lack of understanding of statistics (incorrect use of p-values). There is indeed a cross-effect of psychology replication crisis affecting cognitive science reputation because the term cognitive psychology is used often and interchangeably with cognitive science recently. That's not the only issue for cognitive science, though. Cognitive science has its own study "validity" crisis in that cognitive scientist may find some significant activation in some area and relate it to some other characteristic just because of some correlation. One outstanding example is the study that found significant differences in brain activation between Republicans and Democrats (really?).
Nice book about limitations of cognitive science in current state: http://www.amazon.com/Brain-Imaging-Cannot-About-Consciousness/dp/0199838720
Republican-Democrat brain study: http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0052970
Republican-Democrat brain study debunked: http://www.science20.com/science_20/republican_and_democratic_brains_debunked_hopefully_last_time-119666