Customer support? Yuk!!!!

[#1]

Turning the router off can affect your speeds - depending upon when it is done and how often.
If it is turned on and off several times in a short space of time it is very probable that BT will interpret this as line instability and lower your speed in an attempt to get it more stable.
Noise margins tend to decrease during the evening so if you connect then it is likely that you will get a little lower speed.
If you connect once during the daytime then leave it connected until turning it off for the night it is most unlikely to have an adverse affect.

[#2]

Sorry but I'm going to be bit pedantic here.

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If it is turned on and off several times in a short space of time it is very probable that BT will interpret this as line instability and lower your speed in an attempt to get it more stable.

It's the SNRm margin that is increased which will decrease the sync speed.

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Noise margins tend to decrease during the evening so if you connect then it is likely that you will get a little lower speed.

It's the SNR that tend to decrease in the evening. If the sync has been maintained then the reported SNRm margin will decrease. if the sync has been lost then the system will sync with the same SNRm margin but this will result in a lower speed because of the lower SNR.

[#3]

I think itsme's made a typo there, the SNR decreases.
In plain english Noise gets worse in the evenings generally, otherwise itsme & Jelv have said exactly what I've said time and time again.
You can switch your modem/router off when you like, it's when you switch it on that's important!
Edit: UNLESS you are close enough to the exchange, then it won't matter.

[#4]

I can't see any typo but I will edit so it's clearer when I' referring to SNR or SNR margin.
Sorry you right not a typo more of a brain freeze.

[#5]

Quote from: itsme

Sorry but I'm going to be bit pedantic here. <snip>

I realise all that (subject to Anotherone's correction)  - I wanted to keep it simple. The outcome is more relevant to most people rather than a detailed technical explanation!
There seems to be a myth about never turning the router off. The point I was making is that, providing you a sensible, turning the router off shouldn't be a problem.
I could of added that if like myself you always sync at 8192 and the noise margin never drops gets anywhere near 6db all evening, it doesn't matter if you fire your router up during the evening - again as long as you don't do it too often.

[#6]

Kitz give a good explanation of SNRm http://www.kitz.co.uk/adsl/linestats.htm#SNR_Margin also worth pointing EU to read the target SNR.
I'm just tired of reading posts were a 6dB is described as the signal being 4 times more than the noise. It is if your are referring to SNR it's not when you are referring to SNR margin. So I'm tending to be too pedantic when I shouldn't. Perhaps it's just easier to say the noise tend to be greater at night and therefore will sync at a lower speed.

[#7]

I think that would be clearer to the average poster.

[#8]

How about:
Noise tends to be greater at night and therefore connections made at night may sync at a lower speed.

[#9]

as Graham Bell knows, I have repeatedly asked just that question, now the answertr is a lot clearer