singularity in NDSolve and Table command

Question

We are considering the following equations

m = M/2 (1 + Tanh[v[x]/vo]);
q = Q/2 (1 + Tanh[v[x]/vo]);
M = 2;
Q = 1;
vo = 0.01;
d = 4;
small = 1/10000;
Eqn1 = 1/2 d z[x]^d  D[v[x], x]^2  m - z[x]^d  D[v[x], x]^2  m - 
   d z[x]^(2  d - 2)  D[v[x], x]^2  q^2 + 
   2 z[x]^(2  d - 2)  D[v[x], x]^2  q^2 + z[x]  D[v[x], {x, 2}] + 
   2  D[v[x], x]  D[z[x], x] + D[v[x], x]^2 - 1;
Eqn2 = -(1/2)  z[x]^d  D[v[x], x]^2  D[m, v[x]] - 
   z[x]^d  D[v[x], {x, 2}]  m - 
   d z[x]^( d - 1)   D[v[x], x]  D[z[x], x]   m + 
   z[x]^(2  d - 2)   D[v[x], x]^2  q  D[ q, z[x]]   + 
   z[x]^(2  d - 2)    D[v[x], {x, 2}]   q^2 + 
   2  d  z[x]^(2  d - 3)  D[v[x], x]  D[z[x], x]   q^2 - 
   2   z[x]^(2  d - 3)    D[v[x], x]  D[z[x], x]  q^2 +  
   D[v[x], {x, 2}] + D[z[x], {x, 2}];

When we solve the two equations with a pair of zs, and vs, for example

zs = 0.85; vs = -0.04529;  

we can get the solutions though there is a singularity :

NDSolve::ndsz: At x == -1.00007, step size is effectively zero; singularity or stiff system suspected. >>

But when we run the program

l = 3; zsi = 0.81; zse = 1.5; vsi = -1.5; vse = 0.5; z0 = 0.01;
Table[sol = NDSolve[{Eqn1 == 0, Eqn2 == 0, z[0] == zs,
    v[0] == vs,
    z'[0] == 0,
    v'[0] == 0}, {z, v}, {x, -1, 1}, MaxStepFraction -> 1/11, 
   Method -> {"BDF", "MaxDifferenceOrder" -> 4}]; 
 evz[x_] := First[z[x] /. sol];
 k = FindRoot[evz[lh] - z0, {lh, zs}, MaxIterations -> 1000]; 
 long = 2*lh /. k; CCC = evz[long];
 If[l*0.9995 < long < 
   l*1.0005, {v[long/2] /. 
    sol, (2 NIntegrate[zs/(z[x] /. sol)^2, {x, 0, l/2}] - 
      2  Log[2/0.01])/l}, {0, 0}], {zs, zsi, zse, 0.05}, {vs, vsi, vse, 0.05}]

the singularity will stop the program to run. In this program, we Use the Table command to vary zs and vs, and want to choose a pair of zs and vs that satisfy the condition in the If command. So we must find a way to cancel out the singularity and run our program. This problem has perplexed me several months.

---

IN the First cell, i want to solve Eq1 and Eq2, namely

   sol = NDSolve[{Eqn1 == 0, Eqn2 == 0, z[0] == zs,
   v[0] == vs,
   z'[0] == 0,
   v'[0] == 0}, {z, v}, {x, -1.5, 1.5}, MaxStepFraction -> 1/11, 
  Method -> {"BDF", "MaxDifferenceOrder" -> 4}]

You can run our program, especially the second cell, you will find some numerical problems. I want to solve these problems to run the second cell