Track and update SSH_AUTH_SOCK after reconnecting via ssh. Add this to your .bashrc

authsock.sh

add_authsock() {
    if [[ -L "$SSH_AUTH_SOCK" || ! -e "$SSH_AUTH_SOCK" ]]; then
        return
    fi
    local f c i
    mkdir -p "$HOME/.ssh/authsocks"
    c=""
    for i in $(seq 10); do
        f="$HOME/.ssh/authsocks/$i"
        if [[ ! -e "$f" ]]; then
            c="$f"
        elif [[ "$SSH_AUTH_SOCK" = $(readlink "$f") ]]; then
            return  # already in pool
        fi
    done
    if [[ "$c" != "" ]]; then
        ln -sf "$SSH_AUTH_SOCK" "$c"
    fi
}

update_authsock_ptr() {
    local d
    for d in $HOME/.ssh/authsocks/*; do
        if [[ -e $d ]]; then
            ln -sf "$d" "$HOME/.ssh/authsock"
        fi
    done
}

add_authsock
update_authsock_ptr
SSH_AUTH_SOCK="$HOME/.ssh/authsock"