This paper examines the application of hybrid automatic repeat request with incremental redundancy (HARQ-IR) to reliable mission-critical internet of things (IoT) communications, which frequently use short packets to meet low latency of mission. We first analyze the average block error rate (BLER) of HARQ-IR-aided short packet communications. The finite-blocklength information theory and the correlated decoding events preclude the analysis of BLER. To overcome the issue, the recursive formulation of the average BLER motivates us to calculate its value through trapezoidal approximation and Gauss–Laguerre quadrature. Besides, dynamic programming is applied to implement Gauss–Laguerre quadrature to avoid redundant calculations. Moreover, the asymptotic analysis is performed to derive a simple expression for the asymptotic average BLER at high signal-to-noise ratio (SNR). Then, we study the maximization of long-term average throughput (LTAT) via power allocation meanwhile ensuring power and BLER constraints. To tackle the fractional and non-convex problem, the asymptotic BLER is employed to convert the original problem into a convex one through geometric programming (GP). Unfortunately, since there is a large approximation error at low SNR, the GP-based solution underestimates the LTAT performance in the circumstance. Alternatively, we develop a deep reinforcement learning (DRL)-based framework to learn the optimal power allocation policy. In particular, the optimization problem is transformed into a constrained Markov decision process problem, which is solved by integrating deep deterministic policy gradient (DDPG) and subgradient method. The numerical results demonstrate that the DRL-based method outperforms the GP-based one at low SNR, albeit at the cost of increasing computational burden.