pars = {k1d -> 1, k1r -> 0.1, keq -> 5, eps -> 10.^(-5)}
DAEEqs = {x'[t] == -k1d*x[t] + k1r*(y[t])^2,
      (y[t])^2 == keq*x[t], x[0] == 1, y[0] == Sqrt[keq*1] } /. pars
SetAttributes[StiffnessJacobianMonitor, HoldFirst];
StiffnessJacobianMonitor[i_, method_NDSolve`StiffnessSwitching] :=
  If[SameQ[method["ActiveMethodPosition"], 2] && i < 5,
   If[MatrixQ[#], Sow[#];
      i = i + 1] &@method["Jacobian"]];
i = 0;
jacdata =
  Reap[sol =
      NDSolve[DAEEqs, {x, y}, {t, 0, 30},
       Method -> "StiffnessSwitching",
       "MethodMonitor" :> (StiffnessJacobianMonitor[i,
           NDSolve`Self];)];][[-1, 1]];