It's only considered information overload if you overdo it. Always keep your stakeholders informed, send them status updates on the project regularly, say once a week. Hold regular meetings about the project (every two weeks or every month), answer their emails, handle their queries, do what they ask you for, and you'll be fine.
It's never good to wait until something bad happens to tell your stakeholders, because if you don't talk to them for months and then suddenly you come up with this huge problem that may huge delay the project and substantially increase the costs, their only answer would be, "why didn't you tell us before". Because this lack of communication all this time will imply that you were hiding something... Think about it!