Your question is partially flawed because it is not the oceans that erode continents. Instead it is the collective erosion known as denudation, the sum of all processes inclusing weathering, slope processes and fluvial processes that reduce topography on the continents.
The level to which these processes tend will be the ocean level, identified as the base level. That said a few processes may erode to levels below the base level. Deep weathering could possibly reache below this level but probably only to tens of metres. Glacial processes can definitely erode to kilometers below sea level but this is localised to valleys (probably following fracture zones in the bedrock) forming fjords that may be eroded down to 1 to 1.5 km below sea level.
To add to this general condition, we must consider that sea level fluctuates depending on the distribution of sea basins realtive to continents. New ocean floor is relatively high elevation when compared to older ocean floor due to density differences. Water can also be accumulated on land during cold periods which can cause sea levels to vary. Hence the sea level is far from constant through time.
An implication of the question is what will happen in the future. I will assume the earths interior will cool with time chaning the continental drifting. With slowing drifting mountain building will decrease so that denudation will likely be dominating. A problem here is that we probably need to consider loss of atmosphere and other issues that we do not know much about. There are indictions from Mars that water has been more abundant in teh past yet the topography on Mars is significant because the erosional processes have lost their poser as loss of water may have been critical.
So what will happen in the futiure depends on how tectonic and atmospheric processes change in the distant future due to changes or development in both the earth's interior and the atmosphere in terms of water content (water being a critical componete in both weathering of rocks abnd transport of material in topgraphic terrain).
To conclude, the question is much larger than can first be thought and we need to consider large time frames in which many of existing processes and systems will drastically change. So to provide a time frame is very difficult and essentially pointless.