If the energy of the steam (press/temp) entering the accumulator is significantly higher than the accumulator pressure (steam leaving), then you'll tend to lose water. Think of it as an energy balance. If the energy of the entering steam per pound is higher, you won't need the same mass as that leaving to maintain pressure.
If the energy of the steam entering the accumulator is the same as or close to the steam leaving, you'll tend to gain water. This is assuming you're controlling the accumulator pressure.
The reason you're gaining water in the second scenario is that the steam mass entering is the same as what's leaving but you have thermal energy losses through the insulation that energy lost has to be made up for by additional steam (energy) just to maintain pressure.
The change in water level that I've seen (in both scenarios) is slow. The first was addressed by a small manual makeup line from the feed pump discharge. The second was handled by just blowdown. If the plant you visited was operating in the second scenario (gaining water) the line back to the deaerator might have been so they could reclaim the water. A line just from the deaerator to the accumulator doesn't seem like it would be useful in the first scenario (except for startup but even then I'd think it should be from pump discharge).