Multithreaded TCP server quit when one of the client connection end

Question

I have to do a multithreaded TCP server class that launch a server that can handle up to 4 client at the time but when a client disconnect, the server quit without any .

i have a start function that set all up and launch a new thread with the "server loop" function :

void server_loop()
{
    std::cout << "Server started on port " << port_ << "\n";

    while (is_running_) {
        int client_socket = accept(server_socket_, nullptr, nullptr);
        if (client_socket < 0) {
            std::cerr << "ERRNO: " << errno << std::endl;
            if(errno != 53) {
                std::cerr << "Error: cannot accept client connection\n";
            }
            continue;
        }

        // Acquire a lock on the client_sockets_mutex_ before accessing the client_sockets_ vector
        {
            std::lock_guard<std::mutex> lock(client_sockets_mutex_);

            if (client_sockets_.size() >= MAX_CLIENTS) {
                std::cerr << "Error: maximum number of clients reached\n";
                close(client_socket);
                continue;
            }

            client_sockets_.push_back(client_socket);
            std::cout << "Client connected (" << client_sockets_.size() << "/" << MAX_CLIENTS << ")\n";
        }

        // Start a new thread to handle the client communication
        std::thread(&TcpServer::handle_client, this, client_socket).detach();
    }
}

this create a new thread with the handle client function which is :

void handle_client(int client_socket) {
// loop until the client disconnects
    while (true) {
        // generate a new ID and send it to the client
        unsigned int id = get_unique_id();
        std::string id_str = std::to_string(id) + "\n";
        int res = send(client_socket, id_str.c_str(), id_str.size(), 0);
        if (res < 0) {
            std::cerr << "Error sending data to client: " << strerror(errno) << std::endl;
            break;
        }

        // wait for 1 second before sending the next ID
        std::this_thread::sleep_for(std::chrono::seconds(1));
    }

    // remove the client socket from the list of connected clients
    {
        std::lock_guard<std::mutex> lock(client_sockets_mutex_);
        auto it = std::find(client_sockets_.begin(), client_sockets_.end(), client_socket);
        if (it != client_sockets_.end()) {
            client_sockets_.erase(it);
            std::cout << "Client disconnected (" << client_sockets_.size() << "/" << MAX_CLIENTS << ")\n";
        }
    }

    // close the client socket
    close(client_socket);
}

My problem is that when i connect to it with nc and i exit it using Ctrl+C, all my program exit while I want it to wait any upcoming client.

Do you guys have any clue, from where it could come from ?