Are you sure it is off? Some CRT's click when turning them on (automatic degaussing), but not when they are off. Also, old monitors didn't do this (automatically).
Does it click only a short while after turning it off or does it keep clicking as long as it is connected to the wall?
You should just keep using the monitor until it dies, and replace it them. Maybe it will die soon, or maybe it will keep working for another 10 years.
TheMajorMMX - Intel P200 MMX @ 225Mhz - V-Tech (PcPartner) Baby-AT mb w/ Intel Triton TX chipset - Nvidia Riva TNT2 M64 w/ 16MB - 256MB M-Tec SDRAM - Still running.....