When deploying LLMs in agentic architectures requiring real-time decisions under temporal constraints, we assume they reliably determine whether action windows remain open or have closed. This assumption is untested. We characterize temporal constraint processing across eight production-scale models (2.8-8B parameters) using deadline detection tasks, revealing systematic deployment risks: bimodal performance distribution (models achieve either 95% or 50% accuracy), extreme prompt brittleness (30-60 percentage point swings from formatting changes alone), and systematic action bias (100% false positive rates in failing models). Parameter count shows no correlation with capability in this range-a 3.8B model matches 7B models while other 7B models fail completely. Fine-tuning on 200 synthetic examples improves models with partial capability by 12-37 percentage points. We demonstrate that temporal constraint satisfaction cannot be reliably learned through next-token prediction on natural language, even with targeted fine-tuning. This capability requires architectural mechanisms for: (1) continuous temporal state representation, (2) explicit constraint checking separate from linguistic pattern matching, (3) systematic compositional reasoning over temporal relations. Current autoregressive architectures lack these mechanisms. Deploying such systems in time-critical applications without hybrid architectures incorporating symbolic reasoning modules represents unacceptable risk.