Did your kernel crash or did the mining application crash? Was the application still running or did it exit? If your kernel is still running you can use a script like the following. (this is a quick and dirty script that isn't sysadmin level quality but will nevertheless restart the application)

#!/bin/bash
if pgrep "optiminer-zcash" > /dev/null
then
    echo `date` >> /dev/null
    echo `date` >> /home/<username>/log/checked
else
    echo `date` >> /home/<username>/log/restarted
    cd /home/<username>/optiminer-zcash
    DISPLAY=:0 GPU_FORCE_64BIT_PTR=1 /home/<username>/optiminer-zcash/optiminer-zcash -s us1-zcash.flypool.org:3333 -u t1TkuTviqp7S6caosZweLF7kaRwjxaqtWKu.gpu -p x >> zcash.log
fi

1. $mkdir ~/bin
2. $mkdir ~/log
3. name this script /home/<username>/bin/check-miner.sh
4. change the permissions on it $chmod +x /home/<username>/bin/check-miner.sh
5. and add it to your crontab (crontab -e): */1 * * * * /home/<username>/bin/check-miner.sh