Mira

Same thing happens in kombucha, water kefir, tepache, cider and wine. It is not a kvass fault.

Two other prevention items. Enough salt, following a recipe you trust rather than eyeballing it, because thin brine makes this more likely. And a weight to keep the beets properly under the liquid, since anything sitting above the brine is where trouble starts.

On your actual batch: give it a gentle stir, move it somewhere cooler and taste it in two days. Ropiness does sometimes break down. If it is still trailing off the spoon, it is a fresh batch.