Hydro-fracture in ice shelves is often modelled under hydrostatic conditions, where the water-level within crevasses is pre-imposed. When meltwater supply is more limited, however, water levels may not reach these depths due to a balance between inflow and crevasse widening due to viscous creep induced by the overpressure and far-field strains. When models are used that do capture this time-dependence, these are typically limited to 2D, whereas realistic sources of meltwater, such as surface melt ponds or channels, are localized thus limiting the validity of these 2D assumptions. Here, we present a 3D model for surface and basal hydro-fractures in floating ice shelves that couples fracture propagation with limited meltwater inflow. Fractures are represented using cohesive interface elements with partially saturated flow so the internal water level updates automatically with crack opening, while prescribed surface inflow rates drive pressurization. Simulations show that full-thickness fracture does not necessarily trigger calving: in many cases the crack connects to the ocean and stabilizes instead of propagating laterally, depending on the far-field strain state. For low inflow rates, hydro-fractures can arrest under tensile loading, due to far-field strains widening existing cracks preventing further pressurization. These findings indicate that calving criteria based solely on full-depth penetration can overestimate failure, and that meltwater availability and strain rates jointly control hydro-fracture stability in ice shelves.