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I took a closer look at the issue, saving the game much more frequently than I normally do, so as not to lose anything important. The failed saves started happening more frequently the longer I played, and don't seem linked to combat as I previously thought (one happened when I tamed a moose, for example).

You mentioned the browser version of the game is saved in the browser cache, right? My theory is that when the game runs out of cache space, the saving process cannot be finished correctly, and the game freezes if you choose to save anyway.