Powering Down a Transmitter

I would leave it with its DC supply powered ON.

Investigate is there is a MUTE control. Some BUCs can be put into the MUTE mode to stop transmission. Most BUCs have automatic mute mode if they detect a fault inside themselves such as up-converter Local Oscillator lock failure. e.g "PLL LOCK alarm".

The advantage of having MUTE activated is that any spurious signals leaking into the L band cable do not get accidentally transmitted (such as local radar, radio stations, cell phone etc)

You should definitely not leave it transmitting a low level signal. This will cause interference.

Older, high power HPAs and BUCs that use valve type Travelling Wave Tube (TWT) amplifiers, should avoid switching OFF once the amplifier has been on for several months.  It is OK to power ON and OFF several times during the early months but once ON for 6 months it is best left ON for the remainder of its life - possibly 15 years or more. Reason: The electron beam pushes contamination to the collector end of the TWT and after a few months the cathode becomes ultra clean. Powering OFF and allowing the contamination to drift back onto the clean cathode surface is bad news.  Just my idea !