Basic cognitive functions should not change in terms of the construct, but of course, the distribution might change e. g. to higher means in case of intelligence. Intelligence tests from the first half of the last century still have the same construct as current models when analyzed with approprioate methods.

There are of course aspects, that change, for example things that depend on prior knowledge and vocabulary. Word may become outdated or change meaning. As a consequence, tests relying on outdated words may get inappropriate. Change of meaning: Think f. e. about 9/11. Prior to 2001, this combination was noting special but it received a special meaning due to historical events. What is more, theories may change over time and there the underlying concept is seen in a different way, which leads to changes in the measure development.

In order to test, to what degree tests are comparable over time, there is the method of invariance testing from structural equation modelling. You can either repeat tests with the same sample and assess longitudinal invariance, or you can use different samples and assess it as well.

For literature: Search for the term "Flynn effect". In intelligence testing, this question is very prevalent.