403 forbidden error.
Means that you dont have access to do what you are trying to do. You are trying to access an API endpoint that you dont have access to. Remember YouTube APIs are channel based. This means that you authorize per channel the access.
If you have five YouTube channels and want to see the analytics for each of these channels you will need to authenticate five times and get five different refresh tokens. Each token will only give you access to one channel.
Your issue could be that you are trying to access a channel with an in correct access token.
Timeout
Access tokens expire after one hour you will need to request a new one. If you have requested a refresh token then you can use a refresh token to request a new access token. Remember not to mix them up a refresh token will only give you an access token to access the single account. You will need one for each account you are trying to access.