I'm thinking of starting a Cigar Of The Month Club. Is the monthly subscription club space too saturated?

There are new successful subscription businesses being launched all the time. The question should be is there a market for a Cigar club? You would need to do your own research on that.

One trend I have noticed is that many (but certainly not all) of the subscription businesses seem to hit a plateau fairly quickly and then try to find alternative distribution for their products such as via retail.

Given subscription businesses require little upfront investment, you should be able to validate the idea without spending a huge amount of money.

Have a look at http://www.subbly.co/ and similar platforms that can help you go live and test quickly.

Nothing is ever "too saturated" for a good idea.

The question is, WHO are you marketing to and WHY should they buy from you?

Dollar Shave Club has a different market niche than those who buy from Walmart, or high end buyers who want to go into a store and buy a nice safety razor from a live human with expertise.

What can you bring to the Cigar of the Month idea that isn't just "throwing a cigar you found at them"? Yes, the barrier to entry in setting up a subscription site isn't high. So the competitive advantage lies elsewhere.

A monthly subscription is a great idea for something like that for a start up company. It will allow you to provide the product as the company grows without the fear of not being able to meet the demand. With doing a monthly subscription you want to have several options with that will feature certain brands.

You wouldn't be the first monthly subscription club for cigars. But that doesn't necessarily mean you couldn't acquire customers. I doubt every cigar aficionado who might sign up already HAS signed up.

Personally, I don't smoke cigars. But I own some domain names in the very niche you're considering. I used to pass by several fine cigar shops when I lived in Charleston, SC. So if you want to do reconnaissance, that would be a good town to form partnerships. Lots of tourists passing through, buying cigars – people who might subscribe to such a club.

"subscription" is a business :transaction model for membership, subscription is not a business.
So first and foremost focus on what's your product /offering and make that great, and create a compelling story to tell.
Go get em!

If you have the capital and knowhow to do so - do it.

The one valuable suggestion you need out of this is the following:

Learn about Blue Ocean Strategy, differentiate and stop worrying about a crowded market competition.