Scholarly resources, just like any other resources on the web, are subject to reference rot as they frequently disappear or significantly change over time. Digital Object Identifiers (DOIs) are commonplace to persistently identify scholarly resources and have become the de facto standard for citing them. We investigate the notion of persistence of DOIs by analyzing their resolution on the web. We derive confidence in the persistence of these identifiers in part from the assumption that dereferencing a DOI will consistently return the same response, regardless of which HTTP request method we use or from which network environment we send the requests. Our experiments show, however, that persistence, according to our interpretation, is not warranted. We find that scholarly content providers respond differently to varying request methods and network environments and even change their response to requests against the same DOI. In this paper we present the results of our quantitative analysis that is aimed at informing the scholarly communication community about this disconcerting lack of consistency.