Memories are thought to be stored in synapses and retrieved through the reactivation of neural ensembles. However, neural representations exhibit significant dynamics even in stable environments, a phenomenon called representational drift. Theoretical studies suggest that multiple neural representations can correspond to a memory, with post-learning exploration of these representation solutions driving drift. However, the functional implications of drift-explored representations versus those initially learned remain poorly understood. Here we show that drift uncovers robust, sparsely engaged representations that are otherwise difficult to learn. We developed a method to locally define the non-linear solution space manifold of synaptic weights for fixed input-output mappings with a clipped-threshold-linear activation function. This allowed us to simulate drift as diffusion within this manifold, disentangling drift from learning and forgetting. Our simulations show that sparsely engaged representations---characterized by many inactive and saturated neurons---are more common and thus favored by drift. These representations are robust to weight perturbations and input noise because the activity of inactive and saturated neurons remains unchanged unless thresholds are crossed. However, this robustness comes at the cost of learning, as learning requires feedback on performance changes due to weight changes, which are provided only by engaged neurons. This creates a tradeoff between learnability and robustness: sparsely engaged representations are ideal for maintenance, while densely engaged ones facilitate learning. Drift leads to sparsely engaged representations, promoting transition from learnable to robust regime. During learning we reverse this through an allocation that shifts neurons into the engaged regime for the new input conditions. By combining drift with allocation, we suggest a dynamic solution to this tradeoff enabling memory maintenance and continued learning.