no response when I ping my website, but I can still access it?

Solution 1:

No ping response from your website could mean several things (other than the server having issues) :

Reason 1. You could be behind an HTTP Proxy. In that case the ICMP messages, don't make it out into the internet, so you wouldn't receive an echo reply.

Reason 2. The server has been configured not to respond to ping.

Check using http://ping.eu/ping/. If it does ping, it is just the network you are currently behind that is preventing you seeing ping responses. If it doesn't it is probably Reason 2.

Solution 2:

Most web hosting providers will block ICMP pings by default. This is for security purposes to prevent potential DoS attacks.

There are many services out there that you can use to automate the monitoring of your website's uptime.

Some examples: