With all due respect pvmb, it is NOT a load of nonsense.
First, we'll be clear and get the terminology right. We are talking about Modem/routers not a separate router that are more commonly used on Fibre connections or where someone has chosen to use a custom one on an ADSL line and have a separate Modem (eg.a modem/router in bridge mode).
There are two aspects to this, I'll deal with the most important one first -
If you are on a longer ADSL line, but more especially if parts of the line are overhead, then the line can suffer from sometimes quite large decreases in SNRM between about and hour before sunset to an hour after sunrise - more so in winter. This is primarily due to increases in MW/AM propagation during those times.
If you switch on during those times, because your Target SNRM remains constant, you will get a lower sync speed than you would if you switch on in the day when the actual Noise Margin is generally higher.
For some people on longer lines (depends on the achieved speed), that can make a difference between for example being able to successfully stream video or it buffering constantly, but in any event you have reduced bandwidth.
In addition to that, those on a 20CN connection could drop into a lower profile band and even if they do a resync in daytime when the Noise Margin is higher, it can take upto 5 days before that profile rises if the sync speed goes back up to a new profile band!
There is also the Current Line Speed to take into consideration. Where you've had a lower sync speed and so a lower IP Profile, then the Current Line Speed will also generally have got lowered. Even on 21CN where the IP Profile updates immediately with a new sync speed, BT's servers do not usually forward the increased profile in a timely manner to Plusnet's systems (or any ISP using a BTw product), so there can be a further wait for an overall improvement in achievable speed.
If you are on a fairly short line, or the line does not suffer the effects of MW propagation to any extent, then you may be able to successfully get away with switching on at anytime without noticing any adverse effects.
If you only switch on in daytime, then generally you can also get away with it - however there are some days (any season) where due to atmospheric conditions MW propagation can be high, so you will have a lower actual Noise Margin, hence lower sync speeds if you sync then.
The other aspect is during the 10 day line training. You want to avoid any low sync speeds as it is the lowest speed during this period that sets the Maximum Stable Rate and hence the Fault Threshold Rate. If at some future date you have some sort of fault and the speed is still above the Fault Threshold Rate, then BT Wholesale will not treat it as a speed fault and so you can get lumbered with a lower speed until things get even worse. The other aspect is that if you switch on and off a bit too much during the 10 days, DLM could regard the line as unstable and set a higher Target SNRM, resulting in slower speed.
