I have to break and replace them to get them charging

From what I heard, it only happens when powering them using EU.

This happened to me when I was charging with cefs (eu), and only on the first world start. After world start, if you broke and replaced the energy inputs on the MMs, it would be fixed. This did not happen when I switched to charging directly with conduits (rf). I suspect an issue with MMs on this one.

It's a known issue with ModMachines itself; use RF conduits to supply power as they invisibly detach from EU cables on world restarts.

If it becomes possible to update ModMachines this will hopefully be resolved.

I have to do that every time I log back into my single-player world, but only on the air distilleries.

It seems to me that this issue only occurs when charging them with cables (either RF or EU). Placing a capacitor bank next the energy input seems to solve it.