DIAGNOSIS Intermittent Wi-Fi dropout. The primary cause is interference from the stick's own power supply or competing 2.4 GHz networks.
FIX Methodical elimination. Step 1: Change Wi-Fi bands. Go to Settings > Network > Select your network > Forget. Re-connect, but choose your 5 GHz network (usually has '_5G' in the name). Step 2: If using the included HDMI extender, use it. It distances the stick from potential TV EMI. Step 3: In Network settings, press the Play/Pause button on your remote while highlighting your network. Select 'Change Channel' and try a different Wi-Fi channel.
IF THAT DIDN'T WORK The power adapter is a known source of RF interference. Swap it for a different high-quality 5V/1A USB adapter and cable. Also, in Settings > Display & Sounds > Audio, set 'Audio Output' to 'Best Available' instead of 'Dolby Digital Plus'. This reduces data stream load.
HEADS UP Do not use a VPN on the Fire Stick itself if you have stability issues. VPNs can cause persistent timeouts and are a major source of reported 'Wi-Fi' problems.