Methane is transient in the atmosphere, so if the anthropogenic source stays constant, the methane concentration stays constant.

On the other hand, if the anthropogenic source were to lessen, then the concentration would lessen, wouldn't it?

That's very true... unlike with CO2 there is no significant delay hence methane doesn't accumulate in the way CO2 does. I don't remember the residence time for CO2 in the atmosphere, but ...(google)... it's about a century for CO2 and about a decade for CH4. The latter figure is long enough for CH4 to be well mixed and short enough that even with increased input the effective sinks keep the concentration in equilibrium. The response (eq conc as a fn of forcing) is nonlinear, but in this case the nonlinearity is stabilising (i.e., you don't get explosive growth without a catastrophic event).

Those interested should google on these things a bit, there is lots of interesting stuff on the net. It is easy to stick to scientific (or just multiple) sources.

ciao,
Bruce