Although some of the important consequences of flow-induced entanglement loss in entangled polymer rheology have recently been recognized, this specific molecular mechanism has rarely been investigated quantitatively based on experiments or molecular theories. For the first time, the amount of entanglement loss of a short entangled linear polymer (i.e., seven entanglements per chain at equilibrium) during fast-flow deformation is directly tracked in the stochastic simulation of an existing reptation model. The primary finding is that significant entanglement loss is observed in both fast elongation and fast shearing, and, contrary to some earlier conjectures, is particularly pronounced in elongational flow when polymer chain stretching formally commences. Furthermore, according to the current simulation in which three different CCR (Convective Constraint Release) schemes are considered, entanglement loss appears to have very prominent effects on the elongational rheology of an entangled linear polymer - an observation that had rarely been recognized or considered before. On the other hand, the currently explored features of flow-induced entanglement loss are tentatively linked to a wide variety of peculiar empirical properties of temporarily entangled polymer liquids. In particular, we are thus able to provide a consistent molecular explanation of the fairly well-known phenomenological effects of polydispersity and long-chain branching leading to a pronounced strain-hardening phenomenon, in view of two newly proposed effects of heterogeneous relaxations in preventing, directly or indirectly, fast entanglement loss during flows.