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1.主要是公司网站经常打不开（每天点击频率会高一点）；报错DNS错误
When you get the DNS error, did you open your company website from your LAN? Have you tried open it from external? eg on a smartphone with 3G? If not try it, and let me know the result.
2.每天需要频繁重启路由器和电脑 ，清缓存 才会好。
Do you have a static public IP address from your ISP? Or just a dynamic IP? This is important as it may tell you where the DNS attacks coming from? Internally or Externally.
3.其他高频率网站 谷歌 ，百度 和 TM 也会出现DNS错误。几率较少 ，很快会恢复 ， 不需要重启电脑 路由器。
Does this issue happen on all the computers or just on one or some particular computers. Do the computers have anti-virus protection? Have you scanned them, yet?
4.现在启用 谷歌的 DNS服务 8.8.8.8 ，貌似一下子就好了
Do you have a DNS server in house? What's the DNS server you use before?
5.公司网站域名和空间 不在一家公司 （域名在新西兰，空间在美国）会有影响吗
Have you reported this issue to the domain host service company, yet? If not, give it a try. They may know what been happening.