Admission control is an effective solution to managing a wireless network with a large user set. It dynamically rejects users in bad conditions, and thereby guarantees high quality-of-service (QoS) for the others. Unfortunately, a frequently-varying admissible user set requests remarkable power to continually re-establish the transmission link. Hence, we explore the stability of admissible user set, and formulate a joint long-term admission control and beamforming problem for a network with one multi-antenna base station (BS) and multiple single-antenna users. We consider the downlink transmission in a time period containing multiple time slices. By jointly optimizing the admissible users and the BS transmit beamformers in different time slices, we aim to minimize the total power cost, including not only the power for QoS guarantee, but also the power for user status switching. Due to the NP-hardness of the problem, we develop two (offline and online) algorithms to find some efficient suboptimal solutions. The offline algorithm requires all channel state information (CSI), and solves the admissible users and beamformers in different time slices in one shot, based on successive upper-bound minimization (SUM). To support real-time data transmission, we further design an alternating direction method of multipliers (ADMM)-based online algorithm, which outputs the admissible users and beamformers in different time slices successively, utilizing the previous admissible user set, the actual value of current CSI, and the distribution of future CSI. Simulations validate the performance of the two algorithms, and show that the online algorithm is an efficient practical alternative to the offline algorithm.