Are the walls tile, or a look-alike panel? Not sure from the photo.
A properly built shower won't leak even without the tile up. Do you know what is underneath the tile? What's under that? If they put tile up on drywall, that's a big mistake. Do any of the tile move if you put pressure on them?
If I had to guess, I guess the floor flexes when you stand in the shower and that the seal to the drain has broken or loosened. Sometimes, the pipe actually splits if there is movement after a long time. If the receptor isn't installed level, it could be leaking around the door. Well, it could leak around the door, regardless. Another possibility is if the valve is leaking behind the wall. You could probably check that out if you removed the handle and the escution plate.
Personally, I'd build a new tiled shower using Kerdi from www.schluter.com. I did this for my mother at her house. Check out their site and watch the videos.
If you want help with tiled stuff, including showers, check out www.johnbridge.com.