Yeah, it seems that GPU throttling caused the performance drops that I was seeing. I had my temp limit at 75°C and after changing it to 80°, local hashrates are rock solid. This is a bit strange because actual temps always stay between 65° and 68° and never go above 70°. But right now, I'm perfectly happy with hsrminer. Hashrates on the pool still seem to be more volatile than with KlausT, but overall performance is considerably better. Thank you, palgin. Here are my current settings:

Single KFA2 GTX 1060
Power Limit 60%
Temp Limit 80° (actual temp 65-68°)
Core Clock +150 (actual clock 1366-1455 MHz)
Memory Clock -400 (3402 MHz)

First of all, this is a great miner. I get ~670 kH/s with a single KFA2 GTX 1060, Power Level 60%, Core Clock +150, Mem Clock -400. Note that this miner is extremely GPU-intensive. So if you're mining with a low power level, you can try to reduce the memory clock to get a bit more performance.

But I can confirm that the hashrate drops randomly after a certain amount of time. Sometimes after a day, sometimes after a few hours or even minutes. At first I thought it was an issue with the mining pool but it's really the local hashrate that is affected. A few hours later the hashrate sometimes gets back to normal speed.