I've never encountered that message, though I've heard reports of it. Roku devices ae designed go offload apps once memory gets tight. All Roku devices will do this depending on what apps are installed, as different apps take up different amounts of on-board space.
Again, I would expect things to continue to work, but as I said, I've not encountered that message. If you do get a new device, all of the Roku devices have at least twice the local storage of the 3800 Stick, including the 3810 Streaming Stick+.
DBDukes
Roku Community Streaming Expert
Note: I am not a Roku employee.
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It may be that you need to delete some apps (depending on how many you have).
Before you do, try the following:
ATTENTION: If you still cant load YouTube/YouTube (or other apps):
1) Check for updates: Settings/System/System update/Check now
2) Restore the default theme: Settings/Theme/Restore default theme
3) Use a simple screensaver: Settings/Theme/Screensavers/Roku Digital Clock/Set as screensaver
4) Load YT/YTTV/apps
** EVEN IF YOU ALREADY PERFORMED THESE STEPS, DO THEM AGAIN **