I ordered some Kefir grains online and they arrived looking healthy, at least to my untrained eye. I put them in milk and changed the milk every day for three days. By the last change, they were making a very thick kefir in 24 hours. I decided it was time to try to make a bigger batch, so I used about 6 cups of milk instead of the two cups I was using during the startup phase. I left it for almost 48 hours in near-ideal conditions (around 70 degrees F). When I strained out the grains, the kefir was much thinner than the smaller batches and the resulting kefir tasted like the milk had gone bad. Did I use too much milk? What is the ideal milk-to-grain ratio? Is this the expected outcome if you use too much milk or did something else go wrong?
I've made kefir many times.
When you first start using kefir grains, they take time to recover from not being in milk for a while (ie, if they were sent to you by courier or post) and to adjust to the conditions in your kitchen. It's normal for the first few batches of kefir to smell and taste like the milk went bad.
Instead of going with fermenting the kefir in 6 cups of milk over 48 hours, I would suggest your next batch be for something like 2 or 3 cups of milk over 24 hours. Shorter batch times combined with a smaller batch size means the ferment won't take as long, so there's less time for the milk to go bad if that's going to happen.
I haven't made kefir myself, but this sounds very well explainable from a theoretical point of view.
The reason why the milk in the kefir does not go bad is that the microorganisms in the kefir occupy the ecological niche which would normally be free for pathogens (and plain untasty bacteria) to invade. Obviously, you need a sufficient microorganism density for that. If the kefir colony is too small to change its environment and adapt it to its needs, a colony of something else can win the tug of war and adapt it to its own needs.
I can't tell you an optimal ratio, you'll need to experiment a bit. Also, wash the salvaged grains and place them in the amount of milk which used to work. Only if that works, try gradually increasing the dose. If it doesn't work well, wait a bit to see if your colony is happy enough to grow, at which point you can try to up the milk. Or just get more grains from the seller.