a = {1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2};

b = {{First[a]}};
c = Rest[a];
Catch[
  While[True,
   n = 1;
   While[Total[d = Quiet@Check[Take[c, n],
         Throw[AppendTo[b, c]]]] <= Total@Last[b], n++];
   AppendTo[b, d];
   c = Drop[c, n]]];

b