The mouse stopped clicking at times – it seemed to happen at arbitrary moments. The pointer would still move, but it was no longer possible to click in any way (on my ThinkPad X201 Tablet meaning: trackpoint buttons, touchpad buttons, touchpad tapping, pen input, finger input). The reason for this behavior was probably a defective keyboard (which includes the trackpoint). This post is about temporary workarounds for this issue when it happens though.
The so far least invasive way to re-initialize the mouse (compared to restarting X or rebooting) is to restart the window manager. When you can open a terminal without the mouse working, use this command in a X virtual terminal window [source]:
Alternatively, switch to a console (Ctrl+Alt+F1) and use this command:
DISPLAY=:0.0 openbox --replace