Query: Are the miners and laptop using DHCP or static IP addresses? If they are static addresses perhaps the laptop is using the same address as your router or a miner and causing a conflict somewhere.
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This is a good point but based on this theory and regardless of his set-up the worst result that would come out of an IP conflict would be 1 miner going offline, also if the laptop was using the gateway address as its own IP it can't possibly affect the router the way OP describes.
It's most likely this
Were you using too much bandwidth on your laptop so some machines were dropping hash on dev fee and then they would restart? Or did your laptop just idle?
Just the laptop getting on the network would cause the problems. it wasn't using any bandwidth, it just logged on.
If it's logged in then it's connected to the network, and thus is using bandwidth, I would refrain from using the word bandwidth to clear a lot of confusion, and let's call it "traffic", there is an on-going connection between the laptop and the router as long as they are connected, even if it was sitting there doing nothing, also, it could be doing something in the background such as windows/antivirus update, unless you closely monitor the router's inbound and outbound traffic you can't tell.
With that being said, if your laptop caused that then it's very likely that either your router or internet speed is pretty must at a critical level, so the slightest extra traffic will again cause the same issue, you might want to get a proper router and perbaps a better internet connection, you can't tell where the problem actualy is unless you troubelshoot it.