Where did you buy the replacement battery from? I bought a few times replacement batteries from my laptops and cell phones(from a few different online stores even ebay). I can't argue that they're very cheap compare to the original. But none of them could last. Some of them, after a few chargings, had the same issue like yours. IMHO, the problem is dead cells. Most generic batteries don't have good quality control and even use bad cells those didn't pass the standard for named manufacturers to cut corners. That's how they sell them cheap. So when one or more cells in your laptop's battery went dead (sudden voltage drop), the whole battery doesn't have enough voltage to power your notebook, hence your laptop suddenly died. When you charge it again, the voltage went up abruptly and even the almost dead cell or bad cell will hold some voltage thus it can power back your laptop. Wehn you use it again, that bad cell will lose the voltage again and kill your laptop.

And other ones' holding power dropped dramatically after just a month or so.

For notebooks, I've never wanted to buy anything else but the original. If you can't buy from the manufacture, you can try going to any computer stores and see if they have any generic batteries compatible to your notebook. Those big computer stores's generic batteries are not so bad or else they won't take any risk carrying them. If it's not available also, then try your luck again buying it online. You're really unlucky with your first one. Usually, it works for a few months before went that bad.