Recent work has shown that layer pruning can effectively compress large language models (LLMs) while retaining strong performance on classification benchmarks, often with little or no finetuning. In contrast, generative reasoning tasks, such as GSM8K and HumanEval\textsuperscript{+}, exhibit substantially weaker recovery. We show that beyond surface-level text degradation, pruning leads to a loss of key algorithmic capabilities, including arithmetic computation and balanced parenthesis generation. Under realistic post-training constraints, without access to pretraining-scale data or compute, we evaluate a minimal recovery strategy based on supervised finetuning with self-generated responses. This approach recovers up to 90\% of baseline performance on classification tasks, but recovery for generative reasoning remains fundamentally limited. Notably, even models finetuned on $\sim$400B tokens after pruning fail to recover their original reasoning performance, suggesting that such capabilities are not as easily restored. This limitation persists even on simple tasks such as arithmetic, which do not require multi-step generation. Overall, we characterize the practical limits of layer pruning for generative reasoning and provide guidance on when depth reduction is effective under constrained post-training regimes.