Never, so long as they can keep getting government money to pay them for accomplishing nothing.
In a minute, if they have to depend on money from people who expect to get something for their investment.
I don't know who that was. Ignore him. :-)
I would guess SETI will go on forever, or until they run out of people willing to look -- and I don't expect that will happen, because no matter how slim the odds, the rewards are just too great.
They won't ever find anything though.