Frequent switching on/off a chip/module
Failures due to power cycling are most often associated with Thermal Shock. If the unit is cold compared with its normal operating temperature, then the act of powering it can cause damage, but just how much is somewhat difficult to discern.

There are other failure mechanisms, such as electrostatic stress, but those tend to be associated with (generally) passive components.

If you have a unit that is being switched on and off quickly, but is in thermal equilibrium due to the average power (such as the regulator Andy mentioned because the thermal time constant is very long compared with the switching cycle time) then no thermal shock occurs. 

Thermal shock depends on the rate of change of temperature of a device and the gradients it can cause (although the absolute temperature is also used to compute device failure rates normally using the Arrhenius equation). Long term thermal failures and thermal shock failures are different mechanisms.

In your case, the 3 seconds between power cycling is unlikely to change the temperature in any significant way for any given power cycle, and the unit will eventually achieve thermal equilibrium after many cycles in all probability, so regular cycling of a low power object might well have no problem. 

A clue would be to find the effective self-heating of the device for each power-up and understanding the thermal time constant of the various parts of the device.