This paper investigates the resource scheduling minimizing the packet loss when the wireless communication system operates with Energy Harvesting (EH) based devices. The packet loss occurs when the buffer is overflowed and when the queued packet is older than a certain pre-defined threshold. We so consider a strict delay constraint rather than an average delay constraint. The associated optimization problem can be modeled as Markov Decision Problem (MDP) where the actions are the number of packets sent on the known channel at each slot. The optimal deterministic offline policy is exhibited through dynamic programming techniques, i.e. Value Iteration (VI) algorithm. We show the gain in the number of transmitted packets and the consumed energy is substantial compared to a naive policy which forces the system to send the maximum number of packets using the available energy in the battery.