To make sure the connection is stable, first try an extended ping with a PC on the extension end to the router. For example, if the router's IP is 192.168.88.1, you would type:
ping -t 192.168.88.1 Leave the ping test run for an hour or two, then press CTRL + C to stop it. If you see any packet loss, this could indicate a brief drop in the connection. If there are multiple packets lost, e.g. 10+, try scrolling up to see if there are any clusters of "Request timed out." results as this indicates a more serious drop.
If the connection is stable, you can then try running speed tests between two PCs or laptops if you have two handy. Place one within the network (e.g. attached to the router with an Ethernet cable) and the second on the extension PowerLine. You can then use a utility such as NetStress or iPerf to test the speed between the two over a minute or two to check for any fluctuations.
NetStress is simple to configure and shows a throughput graph. With it running, you can try turning on/off electrical appliances, such as a vacuum cleaner, microwave, etc. to see if there is any fluctuation:
http://nutsaboutnets.com/archives/netstress/