1) seems like a perfect complement to something like mattermatrk: http://mattermark.com/ perhaps try reaching out to those guys? They offer startup tracking so pairing it with this fantasy-investment style game could work well.
2) learning from fantasy football - perhaps you get people to sign up in groups and compete against each other with new money being released into the pool each month/quarter?
3) you could bring people back into the app when the startups they have invested in get in the news? This would involve building a lightweight RSS-scraper and some logic but might not be too hard and would add a nice feedback loop for the product.
4) maybe you let people use (small amounts of) real money to invest in the startups, and let people buy and sell their investments? Kind of like a second market platform? this would make it inherently more compelling for people to stick around but it's almost certainly a lot more work to build...