This code add to your .bashrc file. It is working for multiple sessions. Edited code of GitHub example.

Automatically start ssh-agent on Windows

env=~/.ssh/agent.env

agent_load_env () { test -f "$env" && . "$env" >| /dev/null ; }

agent_start () {
    echo "Starting new SSH agent"

    (umask 077; ssh-agent >| "$env")
    . "$env" >| /dev/null ;
}

agent_load_env

# agent_run_state: 0=agent running w/ key; 1=agent w/o key; 2= agent not running
agent_run_state=$(ssh-add -l >| /dev/null 2>&1; echo $?)

if [ ! "$SSH_AUTH_SOCK" ] || [ $agent_run_state = 2 ]; then
    agent_start
    find ~/.ssh/ -type f -exec grep -q "PRIVATE KEY" {} \; -print | xargs -d '\n' ssh-add
elif [ "$SSH_AUTH_SOCK" ] && [ $agent_run_state = 1 ]; then
    ssh-add
fi

unset env