We analyze quantum correlations in a three-mode Gaussian state generated by a tritter, driven by a two-mode squeezed vacuum and a coherent state. The coherent amplitude does not affect the correlation structure, which is solely governed by the initial squeezing. For five representative local-loss configurations, we compute the resilience of entanglement and Einstein-Podolsky-Rosen (EPR) steering under all bipartite partitions. We reveal that EPR steering exhibits a pronounced directional asymmetry under loss, and its survival can be maintained over a much wider range of loss by confining attenuation to a single mode while leaving the steering mode and the other mode of the steered pair lossless. This tunable fragility identifies loss distributions favorable to one-sided device-independent quantum protocols. We also clarify the distinction between normalized R'{e}nyi-2 log-det correlations and Gaussian steering. Our results turn the abstract correlation hierarchy into a set of calculable loss thresholds for this tritter-generated state.