Fluid antenna systems (FAS) have recently emerged as a promising technology for next-generation wireless networks, offering real-time spatial reconfiguration to enhance reliability, throughput, and energy efficiency. Nevertheless, existing studies often overlook the temporal dynamics of channel fading and their implications for mission-critical operations. In this paper, we propose a dependability-theoretic framework for statistical quality-of-service (QoS) provisioning of FAS under finite blocklength (FBL) constraints. Specifically, we derive new closed-form expressions for the level-crossing rate (LCR) and average fade duration (AFD) of an $N$-port FAS over Nakagami-$m$ fading channels. Leveraging these second-order statistics, we define two key dependability metrics such as mission reliability and mean time-to-first-failure (MTTFF), to quantify the probability of uninterrupted operation over a defined mission duration. We further extend the classical effective capacity (EC) concept to incorporate mission reliability in the FBL regime, yielding a mission EC (mEC). To capture energy efficiency under bursty traffic and latency constraints, we also develop the mission effective energy efficiency (mEEE) metric and formulate its maximization as a non-convex fractional optimization problem. This problem is then solved via a modified Dinkelbach's method with an embedded line search. Extensive simulations uncover critical trade-offs among port count, QoS exponent, signal-to-noise ratio, and mission duration, offering insights for the design of ultra-reliable, low-latency, and energy-efficient industrial internet-of-things (IIoT) systems.