I think what you may be remembering is an old saying about tires not
starters. It wouldn't hurt to remove the starter and disassemble, clean
and lube the bushings. The lubrication will dry out given enough time.
Other than that, electrical connections are the most likely thing to
deteriorate with time.

-jim

I normally hear the term flat spots used more for tires, but a starter
can develop a dead spot.  

Two common things I see that could be happening to you (outside of a
battery issue)

The starter solenoid could be failing or the circuit feeding it.

The starter itself can get a dead spot or have worn brushes.  You have
carbon brushes in the body of the starter that are held against the
commutator by spring pressure.  Here is a picture of a commutator
http://www.btinternet.com/~roland.czerny/commutator.jpg  Each of those
pieces of copper is an individual circuit.  If one fails the starter
will be a bit weaker but you would probably never notice when it was
spinning.  If one fails and the starter happens to stop so that the
brush is against only that one circuit then the starter won't spin
next time you crank.    I don't think this is your problem though as
you normally have to do something to cause the starter to move a
little before it will work again.

In this case I would do two things.  First go through and clean all
the connections up good including those on the neutral safety switch
if it is an automatic.  Second get a cheap digital volt meter so you
can check the voltage next time it doesn't start.

             Steve B.

Trickle charge the battery, as well.

But a battery with a bad cell won't (usually) recover like that.

That's MY number one guess- bad connection at a battery terminal.

 and I have heard that a starter can

A starter can have one winding on the armature burn out so that if one
of the brushes happens to land on EXACTLY that one element in the
commutator, the starter won't run. But it has nothing to do with
sitting. And also, MOST starters from the last 50 years or so have 4
brushes so that it would take TWO dead windings at EXACTLY the right
orientation relative to each other to make the starter completely
inoperative. One dead winding would only make it weak in that particular
spot. Short story- I don't think you have a starter problem.