From the error messages that you get I can clearly make out that you are receiving a slower speed. The first error message itself is the best example for it. Incase youare attaempting to connect to your company/bank website for mails... it could also be to a slow running server or a server which processes too much of requests.
Let me tell you about each error message you get
01. Internet connectivity has been lost
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This means that the connection to your ISP (Internet Service Provider) is lost. Insuch a case you have to reconnect to the server manually or the moderm or router will automatically try to connect it.
02.The website is temporarily unavailable
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The speed again is the factor over here. This means that the browser is attaempting to reach the wenbsite but its gets a timeout.
03. The Domain Name Server (DNS) is not reachable
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Domain Name Server refers to the hosting DNS of the website. Slow speed can cause this.
04. The Domain Name Server (DNS) does not have a listing for the website's domain.
This comes when the domain you are trying to reach by mail or browser is not in the approved list of the domain which you are currently working on.
05. If this is an HTTPS (secure) address, click tools, click Internet Options, click Advanced, and check to be sure the SSL and TLS protocols are enabled under the security section.
HTTPS ans SSL certifications are too closely associated things. A site gets a https identity only when it is approved by certain verification autority like verign for secure transaction. Incase you get such an error it means that thebrowser is promting you for secure transactions.
My solution will be to upgrade your connection to a bretter speed. This may also result if the network connection has a problem, thereby allowing lower bandwidth to individual systems on the n/w.