It could be that the small transformer shorted out somewhere and that it is not able anymore to boost input voltage.
In my tests, despite the small heat sink mounted on the switching transistor, that seemed to be the component that heated up the most.
This is the main reason why I used a multimeter in series with one of the outputs to measure current—the aim wasn't measuring excess heat: according to specifications the device is only capable of providing 200 mA to the outputs continuously and I strived to keep it below this level during prolonged operation. The device has a load-limiting function, but it did not seem to be extremely effective when for example the reaction reverted to electrolysis when immersing the electrodes too much. It might also be that the very small internal multimeter resistance prevented its destruction in my case.
From recent virtual experimentation with electronic circuit simulators, boost converters can very easily provide high peak voltage but are prone to failure. Other converter types with the outputs galvanically isolated from the inputs are more fault-tolerant (and safer) but it seems more difficult to reach high peak voltages with them—at least with a small number of cheap off-the-shelf components.