So, from time to time my keyboard and mouse disconnect. Just like that.
Say I'm writing something and the keyboard and mouse at one moment at the same time stop working (the NumLock LED on the keyboard is still on, and the mouse's red laser is also on). The only thing I can do then is restart.

Oh, also sometimes the mouse just jumps to random points on a line around the screen, clicks randomly and the keyboard inputs one letter forever (the one I pressed last time I was using the keyboard) until I press any key.

However, I've found that xsession-errors has the logs related to what is happening. I've made two versions.
http://paste.debian.net/109489/ (this is the one where the devices disconnect)
http://paste.debian.net/109490/ (this is just after the mouse jumps to random points, but no disconnection is logged there)

Syslog doesn't have anything interesting inside it. I clocked the disconnection time myself and checked.

So can you guys help me out with this?

I think the solution would be to plug them back in

First things first, have you tried a different USB port? Are you using a laptop or a desktop? Could it perhaps be a faulty USB port/USB PCI or PCI-E card?

Have you tried the mouse and keyboard in a different computer? If that's not an option, perhaps try loading a live distribution such as Knoppix on a flash drive with YUMI loader or Unetbootin and see how they work there.

Kind regards