Thermodynamic systems that preserve information against thermal fluctuations face a tradeoff distinct from transmission (Shannon) or erasure (Landauer). We formalize the preservation problem by defining the preservation stiffness $S_κ$, a response function analogous to magnetic susceptibility, and derive the Stiffness-Odds Identity: at optimal allocation, the stiffness equals the ratio of payload to maintenance capacity. This identity is the paper's central contribution. It reduces optimal preservation to a single measurable response variable and provides a substrate-agnostic diagnostic for thermodynamic efficiency -- applicable wherever maintenance competes with payload, regardless of whether the underlying substrate is biochemical, electronic, or algorithmic. For all systems in the diminishing-returns regime, we prove the unconditional bound $κ^* < 0.50$. For the subclass exhibiting smooth saturation with rate parameter $a \in [2,3]$ -- an empirically characterized efficiency frontier, not a universal constant -- the optimum is further constrained to the 30-50% band. We motivate this functional form from two independent physical principles: Shannon error exponents and thermodynamic dissipation bounds. We then illustrate consistency with representative operating points from kinetic proofreading in E. coli and protocol overhead in TCP/IP networks, and specify conditions under which the framework is falsifiable.