How long does it take for a laptop battery to die?

batteries can be bought from ebay and typically cost about 50-80$ cheap for dual batteries

Most batteries are rated in cycles. Without consulting technical material I couldn't tell you how long your specific batter should have lasted, but it sounds like you got a bum one anyway. I would contact the store you bought it from, or try the brand support.

Most batteries are rated in cycles. So a battery might be rated to fully charge and discharge 300 times or so before performance starts to degrade. Aside from a manufacturing defect, which you appear to have. I've seen "2 years" thrown around a lot, but I've had some last less, some last more. It can change with usage.

Be careful of cheap eBay batteries. I've used them, and they work, but never last as long; expect to replace them every year or so. OTOH, you can go to a place like Batteries Plus, pay a good bit more, but then have a good battery that may be better and last longer than the original (i.e. a good, working original, which you may not have gotten).

I have used 40$ honkong batteries for close to 2 years

Dude branded batteries last more than 3 years of moderate to heavy usage.

Regardless of where you bought the laptop. The manufacturer of the laptop will offer the warranty. So long as you have a receipt (sometimes you don't even need one), just contact the manufacturer. They should offer you a RMA service for your laptop battery.

As far as life of batteries goes, your battery died due to some premature failed cells (these are multi-celled lithium batteries). Without premature failures, batteries can last up to a few years (tops) if the batteries are kept at >50% charge most of the time, and the charging circuitry doesn't aggressively charge the cells. A constant temperature (around ambient room temperatures) environment lengthens the battery life too. I think in this area, the automotive manufacturers have done a lot of research to lengthen the lifespan of their hybrid-electric vehicles.