What are the factors to affect Electric Motor life

There is no standard answer. So much depends on ambient temperature, load inertia, non-inertia load and time between starts.
Things the motor manufacturer needs to know, to determine (with reasonable accuracy) the effect of multiple starts include:

Actual terminal voltage at the machine for each start attempt.
Actual load inertia for each start attempt.
Mechanical arrangement for starting (i.e. is the motor direct-coupled to the load? gear-driven? clutched? etc.)
What is the "source" for the machine (i.e. variable frequency drive, soft starter, auto-transformer, or direct-on-line).
If a variable frequency drive, what is the profile for starting (rate for increasing voltage vs frequency, and any changes to the rate based on speed or time). Knowing the variable frequency drive manufacturer will help tremendously here!
If started on a VFD drive, the maximum current applied to the winding(s).
The repair / maintenance history of the equipment (assuming it is not brand new from the factory).
Vibration signature (amplitude and frequency) taken during a "normal" start at the installation: this can aid in determining foundation stiffness and/or alignment issues which may adversely affect machine life.
Ambient temperature at time of start (incoming coolant).
Whether the machine continues to turn (thereby moving air within the machine to help cooling) between starts .... or if the machine is stationary (which means no air movement, and longer between start attempts).

If a machine fails to start, the first thing to do as Derek mentioned is to find out WHY the start attempt failed ... AND FIX IT. Don't keep hitting the "reset" button, hoping to miraculously overcome the problem!