A MIPstart for unconstrained quadratic integer program - Rejected, but no feasible solution found

I am minimising a convex quadratic function over the integer lattice. I also have a secondary linear objective in cases when the convex quadratic function has multiple minimisers over the integer lattice.

A good guess is to minimise the convex quadratic over R^n, (which is solving a system of linear equations) and then rounding off the solution. Typically, this provides a high-quality initial solution. 

However, for a particular instance, and certain chosen values of parameters, my start solution is rejected by the solver with the message "User MIP start did not produce a new incumbent solution". 

I am running hundreds of such instances, and typically setting Model.MIPFocus = 2 and Model.DualReductions=0 runs the fastest. So I use these parameters. 

For this particular instance, in fact, if I set MIPFocus=1, my initial point is accepted and the problem is solved in about 5 seconds. When I set MIPFocus=2, my initial point is rejected and for over 10 minutes no feasible solution is found either.

Can I do something to always force accepting my initial point?

I am pasting the instance as an LP file below.

\ LP format - for model browsing. Use MPS format to capture full model detail.
Minimize multi-objectives
  OBJ0: Priority=1 Weight=1 AbsTol=1e-06 RelTol=0
   0 x[4] + p
  OBJ1: Priority=0 Weight=1 AbsTol=1e-06 RelTol=0
   3 x[0] + x[1] - x[2] + 5 x[3] + x[5] - x[6] + 4 x[7] - 2 x[8] + 3 x[9]
Subject To
 pCons: - 48 x[0] - 45 x[1] - 56 x[2] - 41 x[3] - 58 x[4] - 63 x[5]
   - 79 x[6] - 62 x[7] - 52 x[8] - 40 x[9] + p + [ - 4 x[0] ^2
   + 3 x[0] * x[1] - 3 x[0] * x[2] + 2 x[0] * x[3] + 3 x[0] * x[4]
   - x[0] * x[5] - x[0] * x[6] - x[0] * x[8] - 5 x[0] * x[9] - 4 x[1] ^2
   - x[1] * x[2] - 3 x[1] * x[3] + x[1] * x[4] + 2 x[1] * x[5]
   - x[1] * x[6] - x[1] * x[7] + 2 x[1] * x[8] + 2 x[1] * x[9] - 4 x[2] ^2
   - x[2] * x[3] + 3 x[2] * x[4] - 2 x[2] * x[5] - 3 x[2] * x[6]
   - 2 x[2] * x[7] + x[2] * x[8] - 6 x[2] * x[9] - 5 x[3] ^2
   + 2 x[3] * x[4] - x[3] * x[5] - 2 x[3] * x[6] - 2 x[3] * x[7]
   + 2 x[3] * x[8] - 2 x[3] * x[9] - 3 x[4] ^2 + x[4] * x[5] + x[4] * x[6]
   + x[4] * x[7] + x[4] * x[8] + 3 x[4] * x[9] - 4.5 x[5] ^2
   - 2 x[5] * x[7] - 2 x[5] * x[9] - 3 x[6] ^2 - x[6] * x[8]
   - 4 x[6] * x[9] - 4 x[7] ^2 + x[7] * x[8] - x[7] * x[9] - 3.5 x[8] ^2
   - 4.5 x[9] ^2 ] >= 0
Bounds
 x[0] free
 x[1] free
 x[2] free
 x[3] free
 x[4] free
 x[5] free
 x[6] free
 x[7] free
 x[8] free
 x[9] free
 p free
Generals
 x[0] x[1] x[2] x[3] x[4] x[5] x[6] x[7] x[8] x[9]
End

You can see the absence of constraints above, making every integer solution actually feasible. 

The MST file with the MIPStart values are below.

# MIP start
x[0] -29
x[1] -18
x[2] -11
x[3] -14
x[4] -39
x[5] -9
x[6] -5
x[7] -5
x[8] -20
x[9] 10

My parameters are below:

MIPGap  0.01
MIPFocus  2
DualReductions  0