I think @Ixrec is certainly on the right track. We have yet to find a cure for the common cold because it mutates so much. Wiki says there are over 200 viruses associated with the cold. By the 24th century, with their advanced medical technologies, it could be well more than that.
Now, the transporter works by using a biofilter, which works this way:
A biofilter is a scanning device that analyzes an incoming transporter matter stream for known biological anomalies. When it detects such anomalies, like viruses, it will attempt to remove them from the stream.
Now, it's certainly possible that some viruses associated with the cold would be eliminated, but because it's adapting, it's unlikely that they could specify all the viruses because they mightn't be known.
The other useful piece of evidence is that in 'Datalore', Wesley notes that people 'used' to get colds. We can make this fit what Crusher says that we don't actually have a cure for it. Most strains of the cold probably would be eliminated by the biofilter, but not all of them because it's adapting could be filtered out. When it's detected, no doubt it would be added to the biofilter records, but if that strain of the virus hadn't been previously found, it wouldn't necessarily be filtered out.