Toyota Repair: 1994 Toyota Corolla, using jumper cables, mechanic check

Question
About a year ago, I began having sporadic problems with getting the car to
start.  When I turned the key in the ignition, there would be a click sound,
but no start.  Using jumper cables has always worked - sometimes it takes
about 5-10 minutes of charging before I can start it - other times it starts
up right away.  I took it to my mechanic last November and he checked out
all the electrical components and could find nothing wrong with any of
them, so nothing was replaced.  This problem has continued over the past
year.  Sometimes it will start if I turn the key 4-5 times; other times it needs
a jump start.  It always makes a clicking sound when I turn the key in the
ignition.

About two months ago, I began taking detailed notes to see if this problem
has some kind of a pattern.  Lately it seems to happen about once a month,
ie every 40-50 times I start it.  I use it in a very regular pattern for going to
work and running errands.  The last time it would not start, I actually tried
turning the key in the ignition about 50 times.  At try #27 it started to catch,
but didn't, and ultimate needed an 8-minute charge with jumper cables to
start again.

Usually I can tell when I'm about to have problems with it failing to start
because for the 3-5 times it does start before failing, it starts sluggishly,
sometimes with a kind of choking noise, or else it feels like it doesn't have
as much strength as it usually does.  

Here's a timeline with possibly relevant details:

10/16/07: I had the "cap, rotor, wires, spark plugs and pcv valve" replaced.  
The car had had a rough idle and was shaking at times.  The mechanic
mentioned to me that he had found some loose and broken wires and the
cap, rotor and wires needed replacing.  

11/2/07:  first instance of not starting

11/5/07:  took it to mechanic.  "check battery state of charge, 550 cca
(good).  Check starter output, 10.5 v. (good).  Test alt. output, 14.7 loaded
(good).  Clean battery cables."

11/24/07:  second instance of not starting.

11/26/07:  took it to mechanic.  "test battery, starter, and alternator.  Found
battery weak, alternator and starter ok, connections good, no excessive
draw.  Replace battery."

12/17/07:  third instance - back to mechanic who kept it for several days
but could not determine anything more because the car always started.

Haven't kept track of the dates it doesn't start until recently:  7/29/08 and
8/26/08.

Thanks for any help or suggestions you might have.  I won't take it to the
dealership because I don't trust them - they tried to extract $1200 from me
for work that didn't need to be done.  

Answer
That's a very detailed and concise description of a problem,I'm impressed, unlike some questions I get where I have to ask more questions than I have answers to get information. From everything you have told me I'm going to have a very short answer because I have seen this very same problem many times and it is actually very common on the corollas, the answer is to replace the starter.