We derive theoretical performance limits of densely covered delay-tolerant networks (DTNs). In the DTN model we study, a number of fixed (data collector) nodes are deployed in the DTN region where mobile (data generator) nodes move freely in the region according to Brownian motion. As it moves, each mobile is assumed to continuously generate and buffer data. When a mobile comes within the communication coverage range of a data collector node, the mobile immediately and completely uploads its buffered data to the data collector node, and then resumes generating and buffering its data. In this paper, we first derive analytic bounds on the amount of time a mobile spends without communication coverage. Then, using these derived bounds, we derive sufficient conditions on node density that statistically guarantee that the expected amount of time spent in the uncovered region remains below a given threshold. Additionally, we derive sufficient conditions on node density to keep the probability of buffer overflow below a given tolerance.