How to play XCOM indefinitely?
Solution 1:
The point of the game really isn't to play indefinitely. But there are certain things that will help you achieve an infinite (or nearly infinite) playtime.
1.) Managing panic is about splitting your time between getting Engineers and extra money to equip your soldiers and build new facilities. You'll want to focus on getting your satellites in the air as soon as you can. This means you have to get building them. There are strategies you can use on the internet, but the basics are usually the same. Focus on getting Engineers to lower the cost of the satellites and facilities. Don't build satellites until you have only 21 days left and don't launch any satellites until the day before the council meeting. Also, don't worry about letting a country panic if it's early on in the month. Launching a satellite at the end of the month will ensure you stop the panic. You can also let them continue to panic until the end of the month, since they don't jump ship until AFTER the council meeting. It'll take a bit of luck and planning, but this will lead into step two...
2.) You need to ensure you have a perfect record with the council up until you launch every satellite you can. Once you have full coverage over every continent, you'll be able to catch every UFO as they pass by, which will make it so you don't have to do Abduction missions anymore. (I still get Terror missions, however, for some reason) To accomplish this, make sure you're trying to cover any countries that are panicked first. Then, finish off any continent you have left. DO NOT let satellites sit unused at the end of the month. While it might be attractive to use them to stop panic, the sooner they're up, the sooner you get a raise in your funding. And then panic won't be a problem, because you'll be covering everyone. And if you cover an entire continent, you won't have to worry about an Abduction mission screwing with the threat in a country you already launched a satellite over. REMEMBER: you can only launch ONE satellite to lower panic. Once it's up, if the country continues to panic, there is no way you can control the panic and you'll have to hope for a random mission to lower it. As long as the sky is completely watched by satellites, though, you can intercept every UFO and panic becomes more manageable. Which leads to the third point...
3.) Start building as many Firestorms and fill your hangers with them. The Firestorm will give you interception capability to bring down any ship in the game. With the right weapons installed, you'll shoot everything down you even uncover. You need to do this because...
4.) Make sure you shoot down every UFO so they don't shoot down your satellites. Of course, you could get the Stealth upgrade for your satellites, but this does the trick as well. If you let a UFO continue hanging out over a continent and don't do anything about it, it will bring down your satellites.
After doing those three things, I see no reason why you couldn't just keep doing mission after mission, shooting down UFOs and looting them for sweet Elerium. Though, at the point you can do the above three things, you'll most likely have already beaten Exalt, Gene-crafted a number of soldiers, and progressed an entire squad to Major. You can steam-roll every encounter you come across, at that point. So I guess if that's what you want to do, have at it.