Is my Q_PopulateResponse affecting my responses in my (admittedly complicated) survey setup?

Here's my setup:

1. Links in e-mails sent via CRM containing Q_PopulateResponse values populate the first question of the survey
2. Javascript auto-advances the first page (which contains just the first question), creating the beginnings of a response
3. Respondents can continue on and answer more questions, submit, etc, but if they do nothing else, the response is recorded after four hours (via the survey settings)

Here's what's going wrong:

For whatever reason, it seems that people are clicking links (from the CRM e-mails) multiple times. (It looks like an average of two clicks per person!) When they do so, it seems that each click is being recorded as a new response, even when done within the four hour window, and not as an updated response.

Can anyone think of why this is happening, and how to "fix" it? The ideal would be for the last click (within the first four hours) to be recorded as the one and only response. Why isn't it working that way?

Edit in August 2020: unfortunately, the good idea suggested by @TomG to turn on "Save & Continue" in the Survey Options does not work for this; successive hits to the "Q_PopulateResponse" links create multiple responses to the survey and do not merely update the sam responses, unfortunately.