Yes they stop anyway. It looks like even if I use the pump to feed the pipes, so that they are always full, the pump shows 200 of fluid, few pipes next to it shows 100, but three tiles further the pipes shows 99.9, and that is enough for drills to stop working after they mine the batch of randomyte ...

I found the way to make drills work, it does not solve the bug, but that's a way around it.
All drills work when pipe is 100% full of quicksilver. When it drops below 100% , even if it is 99.9% eventually all drills come to stop.
I hope it helps to find what causes it now.

And I just noticed another thing, if I delete the pipe connecting the drill when it's paused, it starts working immediately, until runs out of quicksilver. But not always, sometimes it won't restart. If it restarts it always mines 10 randomyte even if before disconnecting the pipe drill had 60-70 qu...

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Maybe you're mining ore-patches so fast that your production of quicksilver is not enough and/or it could be that vanilla pipes are not enough (they transfer fluids too slowly)
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No, I just started the game, and noticed this after I built second mining drill

Strange bug, while mining randomite mining drills just stop working. Only works if 1 mining drill is used, but if I build another nearby sometimes second one works for some time, either doesn't mine at all, and after some time my first drill stops too.
Pipes are full of quicksilver though.