If you plan to make Greek yogurt often, then buying and maintaining an heirloom culture is generally the way to go. It's not terribly hard to maintain a culture. Generally, you'll need to feed your culture with new milk about once a week to keep the bacteria happy. The bacteria in yogurt culture are pretty hardy, and it's hard to actually kill them, but following the tips below will help you keep your culture healthier and more active over time.
Keep your culture covered
Sometimes, those who are new to yogurt leave the lid off their culture, or perhaps only put the lid on loosely, because they think the culture needs to breathe. But unfortunately, this can do more harm than good. There are all sorts of bacteria in the air, and you really don't want too many of them landing in your culture and changing its bacterial balance. Luckily, the bacteria in a typical Greek yogurt culture are anaerobic, which means they do not need oxygen to thrive. If you cover your culture tightly, the bacteria will do just fine, and you won't have to worry about contamination from the surrounding air.
Stir your culture well when you feed it
When you add new milk to "feed" your culture, make sure you stir it in really well. Some people like to use a fork, but a small whisk is even better. You need to make sure all of the bacteria in your culture get exposed to plenty of the new milk so they can feed and proliferate. This also helps ensure your starter remains evenly cultured with bacteria, so when you use it to make yogurt, you get a predictable amount of bacteria in your recipe.
If you need a break, freeze it
If you are going to wait for more than a couple of weeks between yogurt batches, it is a good idea to just freeze your starter, rather than continuing to feed it in the fridge. You can simply pour the culture into a plastic container, pop it in the freezer, and leave it there for a couple of months. This won't kill the bacteria; it will just slow them down. When you're ready to make yogurt again, remove the culture from the freezer, let it come to room temperature, and then feed it. You'll be ready to make yogurt again in no time!
Maintaining a Greek yogurt culture is not that hard once you know the basics. Use the tips above to guide you, and enjoy.