It shouldn't stop if it isn't doing anything. Relying on HDD noise is a bad way of testing whether it's actually doing something. If the CPU load is low, then the bottleneck is the IOPS of the HDD.
I can now confirm the HDD was the limitation. I've upgraded from 4 to 12 GB ram, which made it possible to download a pruned blockchain (2.4 GB total with -prune=550) to a ram drive. The result: Bitcoin Core used all CPU it could get continuously for processing blocks. It downloaded at maximum speed once in a while, then stopped downloading for a while, all the time still processing the blocks.
In total it downloaded approximately 86 GB, and it took 1 full day on an i3 (while also doing normal tasks). A huge speed improvement.
I also noticed Bitcoin Core 0.13.0 is more responsive than the previous version. While synchronizing I can now click Send > Inputs and get the popup instantly. This used to take up to several minutes.
All this combined, I'm ready for bigger blocks
