Electrostatic field lines do not form closed loops because they are the path traced by a unit positive charge when they are left free in an electric field. They are also in tangent to the field lines determining the direction of an electric field. So, if the field lines form a closed loop, then the tangent at any point will direct in different directions, and this is not possible. Also, the movement in a unit positive charge is possible because of either force of attraction or force of repulsion. Therefore, the traces should be in a definite path and not in a closed loop.