The varying shape of cold virus serotypes prevents antibodies against one from effectively neutralizing another.

“now the reason we don't have a cure for the common cold is that all of those different serotypes of the cold virus mean that the virus itself has a different shape on its outside and as a consequence even if you've been exposed to a cold and you've developed antibodies against that cold virus the next cold that comes along very likely has a different shape and therefore your body's antibodies to the cold virus it combed successfully before can't latch onto and defeat that next different serotype of the cold virus”