I would:

1. Make sure the connector pins aren't bent or contained with foreign material

2. Try the game card in another DS lite

3. Try another game in your system

If you find out that the game card won't play in any DS, and other games work in your DS, the game card can be replaced by Nintendo, if you bought it in the last 90 days. Call Nintendo at 1-800-255-3700 and they will help you further.

If the game card works in any DS you have tried but yours, and other games will not play in your DS, your Nintendo DS lite will have to repaired. Call Nintendo at 1-800-255-3700 for they can assist you further.

Hope this helps!

I think Linux2Go is right.  This may be a fake game.  A legitimate game stores game save data in a Flash Memory.  Flash memories retain their contents when power is removed.   I took a fake game apart once and found that they (the evil counterfeiters) used an SRAM and battery to store the game save data.  An SRAM requires power to retain its contents (hence the battery).  If the battery dies, you can no longer save your progress in the game.

Try the game in a DSi or 3DS.  If you get an error when you click on the game icon, the game is fake, and you should report it to Nintendo; you can do this here:  https://ap.nintendo.com/report/

Also, Nintendo has a site that can help you identify counterfeit DS games here:  https://ap.nintendo.com/detect/photos/platform.jsp?platformId=1&categoryId=0