The chances are very good that your starter problem is relatively cheap and easy to fix. Perhaps your starter has the same symptoms as stated below. If not, you can still check things out with the part marked “Testing”, and once a problem is isolated, the remaining portion covers disassembly and re-assembly of the Valeo.
Reviewing the symptoms: The starter operates correctly most of the time. When the starter does operate, the engine is cranked over at a reasonable speed and it does not appear that the starter motor is struggling as if the battery is nearly dead. When it does fail, you still hear a clicking noise, every time you press the starter switch. This clicking noise is a rather strong sound from under the starter cavity cover (not to be confused with a small clicking noise which is the starter relay). Most of the time, when it is failing, several successive starting attempts will get the starter motor to eventually operate.
If the above wordy sequence is true, your problem most likely has to do with the starter solenoid (rides piggyback on the starter motor).