Can bottled water become stagnant?

Yesterday I was hanging out with a friend and he noticed how I had a lot of half finished bottles of water all around my room. None of the bottles were left open. He advised me to throw them out because he said they were probably stagnant by now. But I thought this was ridiculous, because they haven’t been there for more then 2 weeks and I bought the case of water probably 3½ weeks ago. He still made me throw them all away. So my question is can bottled water become stagnant? And if it can become stagnant, how long would it take and under what circumstances?