Wait, what? One third of magazines never reach a pair of hands? Do you have a source for this claim?
Lead times to print magazines tend to be long. They could print them quickly, but the cost would be substantially higher. So it can be anything from days (expensive) for topical magazines that don't carry news, to weeks or months (for things like comics, that are often printed in low cost countries). It is/was generally far cheaper to use cheap print options like that, and over-order substantially over expected retailer requests in case of extra demand, than to be prepared to do multiple print runs.
Each retailer would request more copies than they expected to sell, given that they'd take the copies on consignment, and nobody wanted them to run out of copies - more distribution runs was far more expensive than sending them more copies initially. Given that sales for each retailers could fluctuate substantially from one week to the next, that meant a large number of unsold copies.
So there's two large buffers that by design lead to unsold inventory. Usually the only thing that varies is that the size of the unsold inventory varies from issue to issue depending on well they're at forecasting demand.
Most retailers would only get a distribution run once a week (this distributor didn't handle newspapers) unless a particular issue of some magazine proved successful way beyond the norm.
As a kid I used to love that he had that job - we used to get a huge pack of free comics and other magazines every Friday due to fluctuating orders from retailers - staff got to freely pick from anything that was too old for them to take further orders.
http://www.ppa.co.uk/about/activities/environment/ppa-enviro...