The penetration of renewable energy in modern power systems is still increasing. Battery energy storage can rapidly respond to a dispatch order and is expected to provide multiple auxiliary services. However, deep charging cycles have negative impacts on battery health. This paper presents a health-aware long-term operation strategy for lithium-ion battery energy storage participating in the energy and frequency regulation markets. The strategy determines the capacity bounds that can be bid in the energy and frequency regulation markets and updates these bounds every three months, aiming to preserve battery health and increase market revenue. A long-term operational modeling framework is proposed to address the multi-timescale nature, integrating frequency control, energy arbitrage, and the evolution of battery degradation in a holistic model. A nonlinear degradation model is developed to approximate the health impact of main stress factors, which captures the nonlinearity of three-stage capacity degradation process caused by the formation of solid electrolyte interphase film and lithium plating. For intraday operation, a two-scale stochastic programming model is proposed, in which the market bidding and automatic generation control response are simulated in the timescales of one hour and two seconds, respectively. This simulation based method is closer to industrial practice, as it accounts for various factors in BESS operation. For the seasonal update of the capacity allocation strategy, a dynamic programming problem is established and solved based on the nonlinear degradation model and the daily revenue obtained from simulation of intraday operation; the capacity allocation strategy is determined from the renowned Principle of Optimality by Bellman. This two timescale modeling framework captures the interaction between short-term operation strategy and long-term degradation process. Numerical simulations validate that the proposed method can slow down battery degradation and increase lifetime revenue.