Why is this place falling apart?

Tubs and showers, like everything else in this world, eventually come to
the end of their aesthetic and practical life.   Finishes become abraded
by years of exposure to water, household cleaners, and everyday use.  
The abrasion leads to pitting, staining and, for metal tubs, corrosion.

Water: the root of all evil

Frequently, the wall and floor areas immediately surrounding the tub
become degraded.  Flaws invisible to the naked eye permit migration of
water to the support structures directly behind the finished surfaces.  
Water attacks building materials the way nothing else can.

Would wood last forever?

Wood products of every type swell and shrink with the rise and fall of
water content.  With each swell-shrink cycle, the wood grain loses its
strength.  In surprisingly short order the weakened component is no
longer capable of providing stationary support.  Every time a person
walks by, or bumps into a wall, or closes a door, the minute vibrations
act to wreck watertight seals and fatigue finished surfaces.

Water also causes wood to rot, whether continuously or intermittently
exposed.  It is this type of activity that can often be seen on the floor at
the ends of the tub, where water is likely to escape the confines of the
shower curtain.  If you step on the floor by the head of the tub and feel
sponginess under foot, it is an indication of wood rotted by water

Drywall: mush waiting to happen

Water degrades gypsum board (i.e., drywall, “sheetrock”) quickly and
irreversibly.  Even water resistant “green board”, which is gypsum board
on steroids, cannot withstand the patient onslaught of water.  In homes
of a certain age, gypsum board is what lies behind the ceramic tiles of
bath and shower walls.  

Gypsum acts like a sponge.   If water leaks through a tiny pin hole in a
grout line, it gets sucked in all directions, including UP, by the porous
and thirsty drywall.  The wet gypsum looses strength as it expands.  The
expansion movement causes further failure of grouted joints.  The
further failure of the grout joints permits greater leakage. And on, and
on, and on. . .

Last, but not least

Let us not forget that the mortars and glues that hold the ceramic tiles
or fiberglass panels onto the wall depend on two dimensional points of
contact with each opposing surface.  Unlike screws or nails which
penetrate multiple layers of materials, adhesives and cements are only
as strong as the faces to which they cling.  If one face is wet gypsum
that has turned to mush, or wet wood that has turned to rot, the
fastening strength is greatly diminished.  This is when you begin to see
tiles dropping off the wall, or fiberglass panels separating.

Eventually (really, just the blink of the eye to a water droplet),
adhesives, caulks and grouts begin to fail in a slow motion cascade of
dilapidation. Every loss of integrity to a bathroom surface hastens
further demise.

What can I, the innocent homeowner, do about
this tragedy?

The trick is to keep water from coming into contact with the underlying
materials in the first place.  Therein lies the rub.