Based on this estimate, Obama has the second greatest rate of decline, losing 1.6 percentage points of approval each month. Clinton did worse, falling at a monthly rate of 2.3 points. If you look back to the first figure, you see that Clinton fell faster and further, but then rebounded a bit at the end of the summer, making his net change a little smaller (-14) but his overall rate of decline a bit steeper. Obama's chart shows two phases, an initial shallow decline with a bit of a rebound and a more recent decline at a higher rate. Linear fits don't distinguish between these details. But it is pretty clear that based on the linear trend, Clinton fell faster than Obama, contra-Brooks.
What is more interesting is how many presidents managed only slight declines or even gains in the first 8 months. Carter and the second Bush both lost just over a half point per month. Kennedy, Nixon and Reagan all gained, from 0.1 to 0.2 points per month. Eisenhower gained an impressive 0.65 points per month, and the first Bush gained an astonishing 1.9 points per month. So no, not everyone falls off. But yes, Obama has fallen, and quite badly in comparison. Just not quite the absolute worst.
Take a look at the graphs and explanation, as well as the comparisons.