Router off when on holiday

[#1]

Usually when I am away on holiday I switch my router off.  Last time I did this when I switched it back on it connected at a rather slow speed and took a day or so to recover to normal speeds with several resyncs.  Does the exchange equipment realise that the router is off or does it keep trying to connect and assume the line is bad? Would it be best to leave the router powered up when I am away on holiday?

[#2]

I always turn mine off if I'm away for more than 3 or 4 days. Don't just turn it off, do a disconnect through the router interface first, then turn it off.

[#3]

The exchange equipment will remain quiescent until the router is reconnected. It's the router that does the polling.
My target noise margin is usually 6dB. On two occasions in the past I've gone on holiday when my target margin was stuck on 9dB following a fault. On returning home and reconnecting, it was 6dB. 

[#4]

Thanks for the input.  I'll continue to switch the router off when I go away but make sure that I disconnect before powering off.