The polymerization is a Friedel-crafts alkylation, catalyzed by Lewis acids.
Any metal which can react with HCl (generated by reaction of benzyl chloride with trace water) to form a lewis acid (Al --> AlCl3, Fe --> FeCl2/FeCl3, etc.), will catalyzed the polymerization.
If this is, in fact, the mechanism, then to preserve your benzyl chloride:
1. keep it dry.
2. No metals, or maybe only noblish metals, like nickel, etc.