The problem lies in the aircraft type as a whole. Look at it from a car point of view. If you buy a ford escort would expect it break down with little niggles like alternators more often than if you had bought a Rolls Royce. In essence they are the same thing, a metal box with an engine and four wheels that gets you from A to B, but we all know that the escort will go through more alternators than the roller over a 10 year period.
Now apply ths to aircraft, and what you are flying is the ford escort of the skies. If you want total reliability then you have to look at the "Rolls Royce" end of the market, things like citations or other multi million dollar machines. The average driving school teaches in a small average car, like an escort of focus. They are as relaible as they come for that price bracket. In much the same way a flying school uses cessna 150, 172, or piper PA28's for much the same reasons, both accessability from the market as well as ease of use and availability of repairs and spares.
One final thing to remember is that although I have just used a car comparison, in reality the automotive world is light years ahead of general aviation in engine types. Only now are we seeing the begining of the use of common rail, turbo charged diesel engines in aircraft, something that has been in cars for 10 to 15 years already. Looking at petrol engines we are even further behind, I have yet to see a management computer in a light aircraft, other than the one sat in the left seat!!!
In short answer, the PA28 is a good solid trainer that is as reliable as one can expect given it's place in the evloutionary chain.