Error when working with pointer to a pointer in Binary Search Tree functionality

I've got the following code:

#include <iostream>
#include <vector>
#include <cstdlib>
#include <ctime>
using namespace std;
struct Node
{
    int value;
    Node *left, *right;
    Node(int value, Node *l = NULL, Node *r = NULL)
    {
        this->value = value;
        left = l;
        right = r;
    }
};
struct BST
{
    Node *root = NULL;
    void insert(int value)
    {
        cout<<"Inserting: "<<value<<endl;
        Node **current = &root;
        while(*current != NULL)
        {
            if(value >= (*current)->value)
            {
                current = &((*current)->right);
            }
            else current = &((*current)->left);
        }
        (*current) = new Node(value);
    }
    void remove(int value)
    {
        Node *toRemove = search(value);
        remove(toRemove);
    }
    void remove(Node *toReplace)
    {
        if(toReplace == NULL) return;
        Node *toBeReplacedWith = NULL;

        if(toReplace->left == NULL && toReplace->right == NULL)
        {
            delete toReplace;
            toReplace = NULL;
            return;
        }
        if((toReplace->left == NULL) ^ (toReplace->right == NULL))
        {
            if(toReplace->left != NULL) toBeReplacedWith = toReplace->left;
            else toBeReplacedWith = toReplace->right;
            copyAndDeleteNode(toReplace, toBeReplacedWith);
            return;
        }
        Node *current = toReplace->left;
        while(current->right != NULL) current = current->right;
        toReplace->value = current->value;
        remove(current);
    }
    Node* search(int value)
    {
        Node *current = root;
        while(current != NULL && current->value != value)
        {
            if(current->value > value) current = current->left;
            else current = current->right;
        }
        if(current == NULL)
        {
            cout<<"The node didn't exist in the BST";
        }
        return current;
    }
    void traverse()
    {
        rec_traverse(root);
    }
private:
    void copyAndDeleteNode(Node *toReplace, Node *toBeReplacedWith)
    {
        toReplace->value = toBeReplacedWith->value;
        toReplace->left = toBeReplacedWith->left;
        toReplace->right = toBeReplacedWith->right;
        delete toBeReplacedWith;
        toBeReplacedWith = NULL;
    }
    void rec_traverse(Node * current)
    {
        if(current == NULL) return;
        rec_traverse(current->left);
        cout<<current->value<<endl;
        rec_traverse(current->right);
    }
};
int main()
{
    BST tree;
    for(int i = 0; i < 10; ++i)
    {
        tree.insert(i);
    }
    Node  *a = tree.search(6);
    cout<<"found val: "<<a->value<<endl;

    tree.remove(5);
    tree.remove(9);
    tree.remove(2);
   // tree.insert(4);
    //tree.insert(15);
    tree.insert(6);
    tree.insert(22222);
    cout<<"Traversing:\n";
    tree.traverse();
    return 0;
}

For some reason when executing, the program crashes on the insert(22222) while there is no problem on the previous calls and I can't understand why. The problem must be between lines 26-30 and I always put NULL values in the Node constructor so I'm confused why the loop doesn't break.