Please let us know about your Limesurvey version und build. This can be found at the bottom of the admin screen, e.g. Limesurvey 2.0 (130706).

Please also attach your survey for testing.

Please provide additional information as requested.

This could be two things:
If using tokens (and it seems you are doing that) the people can just resume using their token from the original invitation email they don't need a button for that.

When not using tokens, on the welcome page of the survey the button will show where people can continue using the name/password combination they picked theirselves. You can see partial / saved responses in the admin backend.

To prevent timeouts on a survey, you can insert some javascript that triggers a sort of 'keep alive' request (no out of the box solution there). In general you should try to keep response time per page under the server time out limit. Using save / resume could be something that works when people are well instructed.

Please provide some more feedback or we will have to close this issue.

Closed due to missing feedback.