We report fine-grained, deterministic instability in Dynamic Tensor Rematerialization (DTR), an online eviction policy for memory-constrained DNN training, measured on the reference DTR simulator (simrd) using public execution traces. On an LSTM trace, memory budgets differing by 0.10% of unconstrained peak memory select fast and slow execution regimes whose overheads differ by as much as 7.3x; the slow regime is driven by broadly repeated re-eviction of the same storages (evictions per storage rise from 1.33 to 8.27 while the set of distinct evicted storages is essentially unchanged: 5,233 vs 5,236, with the two sets overlapping at Jaccard 0.999). On a ResNet-32 trace, a fine budget sweep reveals a deterministic feasibility inversion: the run is feasible at ratio 0.101, infeasible (OOM) across 0.102-0.106, and feasible again from 0.107. We trace the immediate cause of the OOM to a fully pinned recursive rematerialization frontier that exceeds the budget after every evictable tensor has been evicted. Ablations using the DTR authors' own variants implicate the joint size-staleness scoring term in the observed LSTM instability. We argue these are at least two distinct budget-sensitive pathologies rather than one mechanism, and we separate what is demonstrated from what remains hypothesised. All results concern the reference simulator; reproduction in a production runtime is future work. Code, instrumentation, and raw results accompany this preprint.