Welcome! What do you think of us?
I ran across another site today that hit me up with a survey right on the homepage before I've even done anything yet. Does your site do this? Would you fill out a survey card at a restaurant, before you've ordered anything, been served or tried the food?
Maybe after a visitor has clicked in a few pages you could accost them with the 'can we help you' type of chat popup, altho some people get freaked out by those too. We should engage the customer at their pace and convenience. If a visitor (prospect) requests (via email or web form) info, or certainly if they've ordered something, that's your cue to send some follow up questions.. how'd we do, what didn't you find, etc.
For business owners looking to use a survey as a 'virtual salesperson', I'd suggest having a more direct question, like Need Help? If yes, direct them to your search engine, show them your most popular products/services and or direct them to your FAQs, but anything other than a Survey.
Some may argue that they garner some insight from the few that fill out the form, but not at the expense of other users that you turn away with this tactic. Still want to keep your survey? Then please add a link to it somewhere prominently on your website, as those are hard to find when I actually do want to fill one out.
