Is the survey something you do every year? Or, is this new for you and your Residents? Sometimes, when it isn't new, Residents become a bit complacent. If it is new, maybe they don't understand how valuable their feedback is.
Have you tried:
1. Going on a door-to-door campaign, taking a small goodie bag and asking them to take a moment to fill it out? That way you can personally explain its value.
2. Instead of a lottery drawing (which many Residents may feel like they have no chance of winning) you could provide "coupons" for concierg items, like a Late Rent Pass, tickets to a local college soccer match, hockey match, etc.
3. Placing balloons on doors announcing a chance to win with the survey attached?
4. Posting it on Facebook Page? Emailing it to Residents? Texting Survey Deadline reminders?
5. Giving a Prize for the most creative survey description of how to improve something on/about the property?