I would say your problem is one of interference between your router and Chromecast. Any number of things can cause interference to a Wi-Fi signal even when that signal is strong. These include other Wi-Fi signals on the same frequency/channel and even other devices on the same frequency/channel. You could try changing the channel your router uses, an Android application like Wi-Fi Analyser on your phone or tab comes in useful here to see what frequencies are clear in your area.
Walls and furniture around your room can also make a difference too. Metal pipes in the wall also. Maybe your TV itself is shielding your Chromecast? Is it wall mounted? Does the Chromecast have a direct line of sight to the router?
Hope this helps towards solving your problem.
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