Entropic forces have recently attracted considerable attention as ways to reformulate, retrodict, and perhaps even "explain" classical Newtonian gravity from a rather specific thermodynamic perspective. In this article I point out that if one wishes to reformulate classical Newtonian gravity in terms of an entropic force, then the fact that Newtonian gravity is described by a conservative force places significant constraints on the form of the entropy and temperature functions. (These constraints also apply to entropic reinterpretations of electromagnetism, and indeed to any conservative force derivable from a potential.) The constraints I will establish are sufficient to present real and significant problems for any reasonable variant of Verlinde's entropic gravity proposal, though for technical reasons the constraints established herein do not directly impact on either Jacobson'sor Padmanabhan's versions of entropic gravity. In an attempt to resolve these issues, I will extend the usual notion of entropic force to multiple heat baths with multiple "temperatures" and multiple "entropies".