Methane doesn't have a half-life, but you are correct it doesn't stay around forever. In about a decade it will react to become carbon dioxide and water vapor, which both contribute to warming themselves.

Scientists know this when they state that over a 100 year period, methane traps 32 times more heat than CO2 [1]. This is the number widely cited. Over a 20 year period it is even worse: 104 times greater! Considering we are trying to drastically reduce the human contribution to global warming over the next 10 to 20 years, methane is a great thing to focus on.

Other thoughts:

It is interesting that the cow population only increased 35% since 1960 according to that source. But what about the methane per cow? Some quick searches suggests the slaughter age may have decreased from 3 years to 15 months during that time. They are growing much faster, fed grain that leads to the methane burps. At a minimum several times more emissions per cow.

CO2 only sticks around for 100 years, by your line of reasoning we should just shrug that off too?

[1] http://science.sciencemag.org/content/326/5953/716