Flux-linkage based sensorless control method is well-known and has been widely used in the control of electrical machines. The closed-loop flux observer (CLFO), which is the adaptive combination of the machine voltage and current models, is commonly adopted. It can cover a wide speed operation range and was considered to be able to solve the dc drift and initial value problem associated to the pure integrator used in the observer. However, it is reported in this paper that this popular CLFO cannot always work as expected. In some situations, dc-offsets cannot be removed by this flux observer, causing large system oscillation at fundamental frequency and is very harmful to the drive system. This important issue has not been reported and discussed in the existing literatures of the CLFO. In this paper, this phenomenon is experimentally illustrated and solution to damp this harmful oscillation is proposed and verified experimentally on a synchronous reluctance machine drive system.