Depending on "which" miners are shut down there is some potential for problems - if it is/was possible to shutdown a large percentage of the hashing power of the network then the difficulty to could be too high for the remaining miners to continue the chain (without it being so slow that it's unusable until enough blocks are mined to reduce the difficulty).

There's also the issue that, if governments are seizing the mining hardware, if they gather enough of it they could perform 51% attacks against the chain to effectively prevent it from working.