According to the National Oceanographic and Atmospheric Administration, the reason the divergent plate boundaries at mid-ocean ridges don't result in gaps in the Earth's crust is that when the plates move apart, they allow magma to well up from beneath and form new rock. At each of these ridges, new ocean floor is created constantly, filling in any potential gaps.
Earth's tectonic plates are constantly in motion. When two plates collide, they form a convergent boundary, either buckling or forcing one beneath the other. When two plates move apart, they form a divergent boundary, opening up a gap in the Earth's crust. However, any gap opened in the crust is quickly filled from below, due to the presence of molten magma in the Earth's mantle. Any reduction of pressure caused by the opening of a new gap is quickly filled, producing new material for the Earth's crust.
The magma found at these mid-ocean ridges is usually more viscous than the magma that wells up inside volcanoes. Instead of forming large mountains and islands, ridges usually form relatively flat structures as the plates move away from each other. Typically, a ridge produces somewhere between 25 and 100 millimeters of new crust every year through this method.