I know very little about electronics (E=IR is about my limit).

A relay on the control board for my espresso machine switches power to
the 1200W heating element. Normally, it closes each time power is
called by the thermostat device. But lately, the relay clicks but
doesn't stay closed.

I've checked many possible causes and found only one anomaly.
Resistance of the heating element should be ~ 12 ohms, but a check with
a digital multimeter shows it as only ~ 1 ohm.

Is it likely that the relay is failing to stay closed because the
current drawn by the heating element is too high?

Thanks,

Rick