To answer this you have to define what you mean by 'breaks down'.
By many measures, society is already breaking down compared to 50 years ago. Blatant organised shoplifting. Sexual assaults commonplace and totally unpoliced. Utter disrespect for any form of authority. Appalling behaviour from car drivers. Appalling behaviour from children in schools (I mean the deliberately rude and disobedient ones, not those with SEND), and on and on.
Perhaps a lot of this is to do with living like overcrowded rat in a cage? Beyond a certain level of population density human behaviour degrades? I don't know.
By many other measures, we are possibly decades or even centuries away from break down, if by that you mean the permanent collapse of the electricity grid, the gas grid, the broadband grid, and the water grid.
Or in the slightly shorter term we could measure electric 'brown-outs' and the introduction of food rationing and petrol rationing.
My belief is that Western civilisation is entering its terminal decline, but it will take about 400-500 years and will happen so slowly that we don't even notice.
We are already about 50-100 years into the process.