fade away to nothing(С годами надежда всё слабела, сходила на нет – Over the years hope got weaker and weaker and faded away to nothing – (Michele Berdy).21)
go for naught(The infantry remained pinned down under intensified ground fire and an enemy dive-bombing, so that the whole effort went for naught. 4uzhoj)
peter out(to gradually become smaller, quieter, etc. and then end The campaign petered out for lack of support. The road petered out into a dirt track. The conversation became strained and eventually petered out. OALD Alexander Demidov)
