Clearer sound after reconnecting cables?

I find that sometime when playing my KSA100 the sound gets a bit grainy and when I disconnect and reconnect the RCA and speaker cables, the sound becomes clearer.
Could there be any physical explanation to this finding?
Well, sure.

Tiny amounts of crud and corrosion on the connector surfaces change the resistance and capacitance characteristics of the connection. I'm told that in extreme cases this stuff can even act as a diode.

For years, experienced listeners have been recommending that you unplug and plug back your cables every so often, just to clean them off.
It sounds like you have some dirty connections. Even when my system sounds good cleaning the connections makes an improvement. Cleaning connections includes interconnects, speaker cables and power cords.
Is there a recommended way for cleaning them connectors?
The recommended way of cleaning them? There are more than one, which is typical of course.

The simple way is just to unplug them and then plug them back in. That will wipe some stuff off, probably enough to make a good contact again. Do it once a year when you clean out the rat's nest behind your system.

Another way to do it is more expensive. Use a contact cleaner and wipe the metal surfaces. Some cleaners also protect the surface from crud buildup. One of the most popular is Caig DeoxIT Gold.
To unplug and then plug back in does not clean anyhthing. It just moves stuff around.

As Tobias said, you can buy electrical contact cleaners such as Caig DeoxIt. DeoxIt Pro Gold is designed for cleaning gold connectors. I stopped using Caig products years ago because it leaves a film that can cause an ugly build up.

Radio Shack has electrical contact cleaners that do not leave a film, they just leave a clean surface. I have also tried some of the commercial cleaners with very good results.
I recommend Kontak electrical contact cleaner.
After you clean them, you might want to try using Stabilant 22. It is the active ingredient in what used to be called "Tweek". It is a bonified contact enhancer used in military, communications and IT fields.

It is made by the people at Dayton Wright of yore.