How often should one shutdown a MacBook instead of just closing the lid?
Whether to shut down or keeping it in sleep state (by closing the lid) depends on the time usage in between. The short answer is:


If you use it daily, enter sleep mode is recommended.
If you rarely use it, shut it down.


So let‘s see the difference between each option.

We’ll start with this statement:


  An interesting opinion - cannot find the link for that now - was that shutting down / restarting serves no purpose for macs, except when that is needed after installing or upgrading applications or the system, unlike in Windows, where shutting down was (is?) very important. Also, that macs do periodical system maintenance work during operation and even sleep, which eliminates the need for restart; possibly restarting would even come against all this, etc., and "not shutting down" is in fact a typical differentiating Mac feature. Is this true?


It’s true that OS X has a periodical maintenance script that runs daily, weekly, and monthly. Each script has  a different purpose to remove logs, rebuild whatis database, and bunch of maintenances on user levels. I can say that it doesn’t affect our day to day usage. It’s more like system maintenance to clean up and sort logs.

In fact, for MacBook models, we should decide whether to shut down or enter sleep state by focusing on which method can keep the battery healthy. Healthy in the way the battery can maintain a maximum capacity in its lifespan.

Most of the MacBook models use Lithium-ion polymer batteries which requires low level discharge to get the maximum usage. Based on the explanation by Battery University:


  Similar to a mechanical device that wears out faster with heavy use, so also does the depth of discharge (DoD) determine the cycle count. The shorter the discharge (low DoD), the longer the battery will last. If at all possible, avoid full discharges and charge the battery more often between uses. Partial discharge on Li-ion is fine; there is no memory and the battery does not need periodic full discharge cycles to prolong life, other than to calibrate the fuel gauge on a smart battery once in a while


For the maximum battery health, you should use your MacBook Air at least until the it depletes to ±60% level before you keep it plugged in again.

It‘s okay to just close the lid without harming your MacBook. Beside, it can run the maintenance script on time.

The only time when you should consider shutting down is when you’re not going to use the MacBook for more than 36 hours. Apple recommends to discharge the battery around ±50% before shutting them down.


  If you don’t plan on using your notebook for more than six months, Apple recommends that you store the battery with a 50% charge. If you store a battery when it’s fully discharged, it could fall into a deep discharge state, which renders it incapable of holding any charge. Conversely, if you store it fully charged for an extended period of time, the battery may experience some loss of battery capacity, meaning it will have a shorter life. Be sure to store your notebook and battery at the proper temperature. (See “Notebook Temperate Zone.”)


I know I’ve emphasized too much on battery health in this answer, but instead of asking if shut down or sleep is better, the decision affects your battery health more than the performance of the operating system.

Feedbacks and corrections are welcomed in the comment below.