Could be numerous things. You could check out the shower pan fairly easily if you can remove the grill over the drain. Get a long balloon, blow it up stuck in the drain so a good portion is below the surface (in case there are weep holes in the drain - there should be - you want the plug below the weep holes). Then, using a bucket, fill up the pan to just below the top of the curb. Let it sit overnight and check the level.
If the plumbing is galvanized, then it might need to be replaced, either supply or drain.