How often do techniques/methods that are considered old or obsolete become relevant again?
There are some important examples of techniques and problems being "revived" after having lain dormant for many years. For instance, in my own field, one of the cornerstones of computer modeling was originally derived in the 1920's, and then basically remained undeveloped until the 1970's, when it was brought back in fashion. (It has since been replaced by faster methods, but it is still regarded as the "touchstone" for high-accuracy calculations.)

Similarly, entire fields of research may have been developed before the applications caught up with them. Again, bringing up an example from my own field of research, the class of materials known as ionic liquids was known as far back as the early 1900's, but again were forgotten until the 1990's (or so) when they were "rediscovered" because they were nonvolatile materials and could be used as replacement solvents in the chemical industry. (It also offered the ability to do "combinatorial chemistry," which was also coming into fashion.)

THe point of these examples is that sometimes theoretical and even experimental techniques may be developed in one era, but the ability to exploit the technology to its fullest extent has not yet been attained. Keeping awareness of such methods thus can have some use. Whether it should be taught to every student of a field is a different issue.