I found a fix. The same thing happened to me. Particles would freeze during a render, though they would play fine in the sequence. I tried unchecking Auto Deactivate within the Particle System, which was a good suggestion by someone else, but the particles remained frozen. So along with unchecking Auto Deactivate, I also found that in the Particle System settings, Seconds Before Inactive was set to 0. I changed this to an arbitrary number of 10, since my sequence was less than 10 seconds long, and this solved the problem. So changing the Seconds Before Inactive to a number greater than the number of seconds within your sequence may help.
