I think this is a pretty deep problem.
I've had about 6 game sessions ruined by this and had to repeat areas / zones as I don't save often enough.

I think the only advice I can give is to save every 20-30 minutes as the game it just too buggy to have hour long sessions then to fall victim to this is a killer.

I know they say the game is in beta and we should accept that the quality of the product varies, but sometimes I wish I'd waited till actual release before playing this game.

I can't say there is any pattern to the times the dice roll has frozen the game, as i've said, it's happened to me about 6 times and at various points with various characters.
I don't believe there is any one way to make this happen, it could be any number of factors.

When the bug / glitch does happen, this is the effect:
1. you can't do anything with your mouse, i.e. you can't click on anything and left clicks don't trigger the 'roll' of the dice
2. you can't use the escape key to get to the main menu, so no access to saving / loading
3. hot keys for save / load don't work either
4. you can't switch active players (not sure if that's on the screen ui, but I hoped that was a way out of the dialog, then access save, but no purchase)

anyway, as i've said before, the only advice is to save OFTEN, it can happen on any dice check you have to manually trigger.
I hope the next patch coming out soon will address this bug.