I think I figured out how they run continuously.

It would be a three vat system the centre vat being the one that turns the feed stock into silicon. It would stay at temperture and pressure the whole time. The first vat containing the feed stock would be brought up to the exact same pressure as the centre one, a value would open letting the feed stock in. It would then be made into silicon while the third vat is brought up to pressure. Once done the silicon would be poured into the third vat while relieving the pressure on the third vat, the first vat would be feeding the center one making for continuous operation. Quite the engineering feat!

Just speculating about the pour but maybe the second value missfuctioned or they couldnt get the third vat up to operating pressure but either way it would have been like Bernard said an easy fix