Chemical reactions are typically driven by moving from a high potential energy state to a lower potential energy state. Polymers are incredibly stable because of their binding mechanisms. It takes a relatively large amount of energy to break down those bonds, and when you do, your end product is something far more stable than the original chemicals you started with. Which means it reacts less readily than the chemicals you started with.

Take for example polyethylene, a product we can recycle relatively well. The first reaction gives polyethylene chains of length N. Because they're as long as a polyethylene chain can be, they're as strong as polyethylene can be, and have the best performance characteristics you can expect. Each time they're heated up to be remolded or have contaminants removed, and to a lesser extent just from use and contact with sunlight, some of those chains break. This creates more N/(2^x) length chains. This causes the plastic to get weaker over time. The energy cost to recombine those chains would consume more petroleum than simply creating new plastics, if it could be done at all.