It sounds to me like the tub was not 'set' properly, and over time, has bowed because it is not supported well. The middle is hitting something, and the fiberglass doesn't have enough strength to hold it up on the ends, so each end is sagging. This would leave water at one part, since the bottom is no longer sloped to the drain. If the drain end sunk, the drain piping may be stronger, and is trying to hold that end up, but the tub is bending.
First thing I'd do is take a long straight-edge and a level and see how the edges and base of the tub are. The edges should be level both along the length and side to side, and the base should slope from one end to the drain.
Once the fiberglass has taken a set, it may not rebound. To fix this, you may need to replace the tub. Many tubs work and last longer if they are initally set in mortar so that they are well supported. This becomes even more important when the subfloor isn't level and smooth.
It's also possible that the subfloor and structure has settled or has water damage, which allowed the tub to sink. If the tub's panel is not removeable, you may want to poke a hole in the wall of an adjacent room to try to look underneath it to get a better idea what's going on.