I have had this tube of MX4 since 2013, it's served me well, countless rebuilds of my computers, CPUs and GPUs alike, home servers, gaming computers, laptops, games consoles, pi4, I used this on everything. You served me well.
8th June 2013 to 4th November 2023.
This really depends on how the particular paste is made. I've never seen MX-4 (carbon) or NT-H2 (ceramic) de-emulsify.
It's not something you'd visually notice all that well. Just that the carbon particles (using mx-4 as an example here) will drift downwards instead of being equally dispersed in the paste. That can leave your solution you apply having too little carbon to do its job as well as it should.
No pastes are just liquid. They're all super finely ground solids suspended in a liquid, and the solids never weigh the exact same amount as a liquid, so given time, the always start to separate.