Tube Life and the Mute Switch

Muting is just that, AFAIK. It just disconnects the output (or input, on my Joule amp) jacks from the signal chain. Anything else is still live. But for final answer, check with manufacturer. Some tube gear has a standby position which keeps the tubes heated but no high voltage. That actually preserves tube life by preventing shock of sudden start up.

2000 hours on a set of tubes?!!

I couldn't find any reference as to the tubes used, but I'll assume that these are either of the 6922/6DJ8 or 12A*7 family. I don't know the circuitry design, but NOS varieties of these families of tubes should be good for 10,000+ hours in most circuitry designs, from what I've been told. What gives?

Fatparrot, the Audio Research website does not use NOS tubes in their products at the factory.

Below is the exact language in the manual regarding tube life expectancy and the use of the muting switch:

"For superior sonic performance, a warm-up period of one hour is recommended. In addition, our PH3 may be safely left "ON" contiuously for maximum performance at all times, but at the expense of higher maintenance costs (more frequent tube replacement). When not in use, simply use the "MUTE" switch. The PH3 draws less wattage continuously than a 60-watt light bulb."

"The vacuum tubes inside your PH3 are 6922 dual triodes, and with normal use should not need to be changed for approximately 2,000 hours of use."

I don't keep my tube amps charged up when I am not at home. Too many things can go wrong and I want my home to be there when I want it to be.

Swampwalker is correct.
Mute only shuts down the output so if a tube(s) go(es) bad the rest of connected on equipment will not possibly suffer from overloading.
To a tube life it nearly makes no difference.