Try updating the firmware on the Blu-ray player to see if that helps. Make sure you have no other issues on your network that would cause your blu-ray player to hang like it is doing. If neither of these solve your issue then yes a new video streamer would help. Netflix software is just like any other software-- at some point it is outdated and needs to be replaced. Unless you still use physical discs however, just go with an Apple TV, Roku, Amazon Fire or something similar instead of a new blu-ray player.

We do still use discs. How to update firmware on player? Nothing else hangs up, and Netflix is ok on the computer. Must be the old machine.

There should be a function in the player's menus to check for a firmware update. It may also do that automatically, in which case if it hasn't in some years then there may not be any further updates available. My Samsung player is outdated for updates but still works with Netflix. It no longer works for YouTube and Pandora since a change in their network security protocols. It originally supported a fourth streaming service (I don't recall which) but that one was removed by one of the updates.

I'll also add, run a network cable to your streaming devices where possible. Sure it's not as convenient as wireless, but it's significantly faster and much less prone to issues.

You might also want to google your player's model number and netflix to see if others are complaining of the same thing. If it's a common issue, you may be out of luck. But others may also just note to update the firmware as already mentioned here.

If nothing you try solves your problem, then a new player, or as already mentioned, a dedicated streaming device like apple TV/roku, etc will fix your problems and give you more usable streaming options.