Shift turns on by itself using the Sticky Keys accessibility feature

I have to use the Sticky Keys accessibility feature, and by and large it works as it should, with one annoying exception: the Shift key goes "sticky" by itself as if I had pressed shift once. There is no icon displaying on the screen that normally indicates it, nor is there the indicator sound, but the computer functions like the shift key was pressed down. I can turn it off only by pressing the shift key thrice. This happens utterly randomly - sometimes I can use the computer ok the whole night, sometimes it happens every five minutes, and I haven't been able to figure out what could cause it.

I have a Kensington Expert Mouse, Logitech MX510 mouse and Logitech Cordless Desktop Pro keyboard.