ORIGINAL: Bebop Cola
While the player controls how many mining stations are built, maintenance for the stations are paid for by the Civilian side of the economy.
I'm no expert on the economics of the game, but here is how I understand it:
The civilian economy get its revenue from "economic activity" on your colonies This economic activity is somewhat abstract, but is related to the population of your colonies. From this revenue are subtracted taxes at those colonies, maintenance costs for the civilian fleet and mining stations, and the cost of fuel purchased by that civilian fleet. Any surplus goes to building a balance for the civilian economy, similar to your balance as the state economy, and from this balance are purchased new civilian ships as needed.
What this means is that you can build as many mining stations as you like, but too many can strangle the civilian economy due to rising maintenance costs. Additionally, building more mining stations tends to promote the purchase of more civilian ships, which also incurs additional expenditures for both maintenance and fuel on the part of the civilian economy. As the civilian economy runs out of money, you might see mass scrapping of civilian ships, and certainly no additional construction of new ones. The civilian economy can't scrap mining stations, however, so it's stuck paying for them even if it can't afford anything else.
When one should stop building mining stations is somewhat subjective and depends on how many colonies one has and how large those colonies are, and how many ships they and their civilian economy are building. Basically, how many raw materials they need. And, of course, more mines means more mines to defend, or more expensive mines that can defend themselves.
It's all a balance. Personally, I try to build as few as possible. It keeps my costs down and I like to think having some scarcity promotes more robust trade with other empires. Then again, it sucks to run low on a given resource when in a pinch. I try to maintain at least one supply of the most important strategic resources but rarely concern myself overly much with luxury resources. I figure the AI can mine those and I'll trade for them.
Well what if my private sector is swimming in cash? Any reason to not just set the construction ships on auto at that point? You don't have to defend the mines if you have 5 of them instead of 1 of them also...