The damaged leaves won't 'heal' and become green again. I suspect there may be some root rot going on, as a result of overwatering. As new roots grow, new damage should not occur, but that may take a couple of months to determine.
An alternative problem could be that it's root bound, and needs to be repotted. From what I can see in the picture you posted, the pot looks okay. I can't see how tall the plant is, though, so the actual situation may be different than what I can see.
The way it works is this: too much water causes the fine feeder roots to decay, which makes it impossible for the plant to take up sufficient water, causing the leaves to brown and, eventually, die. However, if the roots are too crowded in the pot, the soil cannot hold water long enough to allow the roots to take up sufficient water. The result is the same browning and dying of leaves. You can't really tell which problem you're dealing with by how wet the soil is, because in both situations, the surface of the soil will stay moist.
If you're capable of handling the plant, you can look at the bottom of the pot to see if roots are visible in the drainage holes. You can also remove the plant from its pot and look at the root ball, to see if there are a lot of roots wrapped around the outside. Either or both would indicate that the plant needs to be in a larger pot.
On the other hand, if the soil smells sour and/or the fine feeder roots look or feel mushy, then you're dealing with root rot.
"Isn't it enough to see that a garden is beautiful without having to believe that there are fairies at the bottom of it too?" - Douglas Adams