I took the mechanical relay off and disassembled it. From an un-scientific and entirely empirical observation, I suspect it was the culprit:
Luckily the contacts were the only affected part, the coil still works fine. The contacts obviously got very hot when left closed (on) while the machine was refilling and re-heating after I used it for hot water. I cleaned the contacts and the machine is working again, cycling on and off between 1.0 and 1.3bar.
This is a temporary solution. I already sent out one email inquiring for a replacement relay. I am unfamiliar with SSR's as Eric mentioned. Can anyone guide me through this? I am competent with electronics but have never tried such a thing before. I am willing to try if it seems reasonably easy and not too expensive. Otherwise, a replacement relay is fine as long as I can find one and it is not exorbitantly expensive.