The reason we cannot find a cure for the common cold is because viruses mutate rapidly. Where do the mutations occur in the DNA/mRNA of viruses and does this have any effect on the protein level? what has to change for the virus to be considered a new strain?
I don't know if this is a comprehensive enough answer, but viruses are taxonomically broken down into order (-virales), family (-viridae), subfamily (-virinae), genus (-virus) and species. This system was developed by the ICTV and is concurrently used with the Baltimore System.
A lot of species contain variations called virus strains. There are two types, serotype and genotype.
In serotypes, the differences are detected by variation in antigens. Genotypes are detected by differences in genome sequence.(1).
The reason a vaccine is difficult to create for the common cold, or upper respiratory tract infections is not only because of the frequency of mutation but also due to the large number of serotypes present.(2),(3).