I have an older LG TV but it does have HDMI ports. I have the Roku Streaming Stick + and my TV was giving me invalid signal no format errors and would flash the roku briefly. Made it to the video settings and changed it from 1080 to 720 and that fixed the problem, until I turned the TV off. Then it reverts back to not working. Why is it doing this? I should not have to leave my TV constantly on, or keep resetting and reinstalling roku every time I want to watch TV.
I don't know why your Streaming Stick+ is not retaining the Display type settings, mine retains settings without an issue.
The only thing I can suggest is perhaps the flash memory is faulty and loses data when it is powered down. If this is the case and if you are powering your Roku via a USB port on your tv that shuts down when the tv is turned off, that would explain why your Roku loses this setting when you shut down the tv.
If that is what is happening, try powering your Roku by plugging into your house power via a USB power adapter. This will keep the Roku powered up so that the setting is retained. If you don't have an adapter from Roku, an extra from another device can be used, as long as the fine print on it says the output is at least 1 amp.