You could define a start/end date via attributes, and then have a script/cronjob call the LS mailing functions or have mails with tokens sent uppon the start/end attributes.
Howver, if the surveys should be re-sent every week, then it would be a good start to script that, so a new token is generated uppon finish of a survey, and then sent to the user at the correct date.
I have written an interface to LimeSurvey, over which one can send via XML start/end dates of surveys and specific attributes. The participants are automatically mailed, and remindered. If interested, feel free to visit
www.dreifragen.net
, or I can also give you directions on how you can accomplish such a feature by your own coding.
Regards
Gregor