Q: iMac keeps loosing internet connection but not wifi connection

Reset both the modem and router.

Do you have both Ethernet and wifi connected at the same from the iMac?

From OSX terminal can you execute nslookup www.google.com and get a valid response when your Safari says your are not connected? You can try changing to Google DNS at 8.8.8.8 or OpenDNS and see if it is a DNS issue or not.

Please test after taking each of the following steps that you haven't already tried. Stop when the problem is resolved. Back up all data before making any changes.

Step 1

Take the applicable steps in this support article. The Wireless Diagnostics program generates a large file of information about your system, which would be used by Apple Engineering in case of a support incident. Don't post the contents here.

Step 2

Disconnect all USB 3 devices. If you don't know which are USB 3, disconnect all USB devices except keyboard and mouse.

Step 3

If you're not using a wireless keyboard or trackpad, disable Bluetooth by selecting Turn Bluetooth Off from the menu with the Bluetooth icon. If you don't have that menu, open the Bluetooth preference pane in System Preferences and check the box marked Show Bluetooth in menu bar. Test. If you find that Wi-Fi works better with Bluetooth disabled, you should use the 5 GHz Wi-Fi band. Your router may not support it; in that case, you need a new router.

Step 4

Open the Network pane in System Preferences and make a note of your settings in the Wi-Fi service. It may be helpful to take screenshots of the various tabs in the preference pane. If the preference pane is locked, unlock it by clicking the padlock icon and entering your administrator password. Delete Wi-Fi from the service list on the left by selecting it and clicking the minus-sign button at the bottom. Then recreate the service by clicking the plus-sign button and following the prompts.

Step 5

Reset the System Management Controller.

Step 6

Reset the PRAM.

Step 7

Launch the Keychain Access application. Search for and delete all AirPort network password items that refer to the network. Make a note of the password first.

Step 8

Make a "Genius" appointment at an Apple Store, or go to another authorized service center.

Have a possible similar problem after upgrading to 10.9.4. Using only Ethernet cable, turned off wifi. Some time after a reboot  a Chrome or Safari browser cannot connect to web sites (even not to the local router admin page using IP address). Since both Chrome and Safari behaves similar it is unlikely a browser problem? But here is the thing: I can ping an Internet host from the terminal without problem! DNS lookup for the ping works fine.

So a question to you is how do you detect dropping the Internet connection? Is it by not being able to connect via browser to web sites? or otherwise?

Any suggestions what to do when I am in the situation with no web communication but being able to ping Internet hosts?

You can try

1. telnet www.google.com 80

2. Use OSX terminal and run curl.

3. If possible, run a network packet capture tool.

4. What type of equipment is between the NIC and the ISP gateway?

If you cannot get to the router web page from the local LAN, do you have any firewalls, or possible route issues. Ping is a reasonable test, but not a very good test of network reliability.

Good suggestions, I will try 1 & 2 next time I lose web connectivity. Have a Netgear Nighthawk R7000 router and a ADSL modem. However I can ping the router, just not connect via http, so I don't think there are routing problems either. Mac firewall is turned off. I will check routing table as well just to be sure.

Problem solved! Un-installed Sophos AV 9. Found in other threads that this has been a problem before (snow leopard) and gave it a try. Web connectivity was restored immediately, once removed! Maybe something in the 10.9.4 upgrade that didn't play nice with Sophos.

Might not solve the OPs problem though. Should be posted under the more generic "can ping but not browse mac" label.