Leaving the sub on permanently uses a little more juice and increases the length of time the capacitors inside are exposed to heat. Left on long enough and with enough heat then the caps can dry out. When they're dessicated enough then they'll fail to charge from cold and the sub's self diagnostic circuits will prevent the sub coming on.
Caps drying out was a big problem in TVs over the first 15 years of the century. It was a combination of poor design layout and shoddy capacitor quality due to cost cutting in manufacture. The test for bad caps is visual - they bulge at the top or bottom - and also a heat/chill test. Once warmed up, a borderline failure will work for a while. Chilled down it stops working.
Subs didn't suffer the bad caps problem so much because the capacitors being used are quite large; about the size of a C cell or D cell battery. The caps in tellies were much smaller - Biro thickness or less and about 1cm long - but used in large volumes so a small percentage saving made a big difference to the annual parts bill.
Big question then...... Will you kill your sub leaving it on. Answer: Immediately, no. In 3-5 years, very unlikely. Longer than 5 years, possibly. However, out of all the customers I've known I've only come across one with a dead sub, and that was a trade-in to me which I fixed for £20.
Your other option is switching the sub off manually when not in use. It's debatable which would do more harm. Electronics are said not to like going from fully off to powered up. Repairing two obviously-goosed caps is a simpler fix than fault-finding on a whole board, so I'd go with keeping the sub on out of the two options.
Next we look at why the sub is clicking on and off.
The auto-sensing circuit uses the difference between the signal level and ground level on the audio input to tell if there's an audio signal present. After use where there's no signal for 15-20 minutes, the sub should go in to standby. You'll hear the power relay click. It'll click again when the power goes back on. That's all pretty straight-forward.
Where issues occur is if the signal level is low compared to the background noise level on the line input, or where the noise level is high compared to the signal level. In both instances there's not enough difference between signal and background level for the sub to tell if there's signal present. However, the causes are often different.
Insufficient signal is easy to fix. If the sub's own volume control is turned up too high, then when the AV receiver runs the auto-calibration routine it'll have to reduce to output level going to the sub to get it to balance with the other speakers. You'll see this in the speaker set-up menu; the sub will have a bigger minus number compared to the +/-dB figures for the other speakers. The solution is to turn the sub's own volume control down, then rerun the speaker auto cal' wizard.
Too much background noise is harder to track down and fix. The biggest cause is bad subwoofer cables. More specifically, it's cables with insufficient shielding to stop or drain away the effects of radio frequency interference.
Sadly there's too much B.S. surrounding cables. Good cables don't have to be expensive, they just have to be engineered right. Price is no guarantee of performance though. All too often the people and companies selling cables haven't a clue what makes a good cable, nor do the know what's inside the cables they sell to tell if it's good, bad or indifferent.
If the issue with your sub is simply the occasional click - and it should only be after starting some sound playing, and about 20 minutes after the end; that is unless you take a break - and it's annoying you, then leave the sub switched to permanent on.
On the other hand, if the sub isn't coming out of standby, or it's dropping in to standby during viewing, or it's switching on and off at random even when the audio gear is switched off then come back to us.
