WSAD Movement performs unwanted flipping of character

I am making a 3rd person shooter game, and the following script part is supposed to handle the character's movement and animation (I have a rather old type of model available for my game's purposes), using the Arrow Buttons or the WSAD keys. It is supposed to simply apply rotation (left/right) to the character while moving it forward.

 void AnimMovement()
     {
         //We receive the raw values for the Horizontal and Vertical input axes (-1, 0 or 1)...
         var movementV = GetInputValues();
         float h = movementV.first;
         float v = movementV.second;
 
         //And the current state of the player's animator.
         var curState = playerAnimator.GetCurrentAnimatorStateInfo(0);
         
 
         //For optimization purposes, if there is no input (h = v = 0), then we return here.
         if (h == 0f && v == 0f)
         {
             //We are not moving.
             playerAnimator.SetFloat("Speed", 0f);
             return;
         }
 
         
         //if (h != PrevH)
         playerAnimator.SetFloat("Speed", 1f);
 
 
         //We will move our player, only if the current state of their Animator is the LocomotionState.
         //This is to prevent our player from moving when dead.
         if (curState.shortNameHash == Hashes.LocomotionHash)
         {
             cc.SimpleMove(transform.forward * speed);
         }
 
         if(tag != Tags.AIPlayerController)
             ApplyRotation(h, v);
 
         PrevH = h;
         PrevV = v;
     }
 
     void ApplyRotation(float h, float v)
     {
         //We need to be able to turn around the Y axis using the arrow/WASD keys,
         //so we'll make a rotation that enables this.
         float turnVal = (h == 0f) ? v : h;
         tiltZ = Utilities.ClampAngle(tiltZ, 0f, 360f) + turnVal;
         Vector3 lv = new Vector3(h, 0, v);
         var nrot = Quaternion.LookRotation(lv,transform.up);
         transform.rotation = Quaternion.Slerp(transform.rotation, Quaternion.Euler(transform.rotation.eulerAngles + nrot.eulerAngles), Time.deltaTime * turningSpeed);
     }
 
     Pair<float, float> GetInputValues()
     {
         float h, v;
         if (gameObject.tag == Tags.PlayerController)
         {
             //PlayerController input.
             h = Input.GetAxisRaw("Horizontal");
             v = Input.GetAxisRaw("Vertical");
         }
         else
         {
             //AIPlayerController input.
             h = nav.nextPosition.x;
             v = nav.nextPosition.z;
         }
         
         return new Pair<float, float>(h, v);
     }

The problem is that, while at first the character moves well, after a while it simply goes upside down. I suspect it has something to do with the rotation being applied to the character, but I am stumped.

Does anybody have any idea why this is happening?