Brake lever shifters
 

I purchased a Marinoni bike and am experiencing problems with the Ultegra Brake lever shifters, Model 6500.
Looking on the internet, it appears that these are not terribly durable. Since there seems to be issues with the derailleur and chainwheels when replacing these things, I'm not sure what to do. I would prefer to replace them with something more reliable. The right shifter is actually ok yet, but the left won't shift down to the smaller chainwheel unless I use 2 hands. One to hold the larger lever and one to push the smaller one.
There are 2 chainwheels and a 9 speed cassette. Any suggestions would be greatly appreciated

What issues have you been told you would have with the cassette and/or chainrings if you were to replace the shifter? I'm having trouble figuring out why you should have issues with the cassette and/or chainrings with a bad shifter.