When there are multiple sources for a WiFi signal, which is the case when you are using a WiFi extender there are at least a couple of factors that will determine which source your device will attach to.
  1. Signal strength — the strongest signal will always be preferred.
  2. Signal to noise ratio — if for any reason when signal strength is not too widely different the signal with the hightest ratio of signal to noise will be preferred.

Those values can change from minute to minute and even second to second so if the signal strength and SNR are close it is entirely possible the connection may switch from one to the other. In your case where the connection is switching back to the router that is creating the network that could be interpreted as indicating the extender is not providing any real benefit for you. (If that sounds pretty cautiously worded — that was my intent.) Assuming your computer is located where you are watching the videos that are hanging/pausing/etc., what does Netspot tell you the level (SNR) is from the router and from the extender?

If we knew what it was we were doing, it wouldn't be called research, would it?

— Albert Einstein