That model wasn't widely released in the US. I'm assuming you're in UK or EU? Or did you buy it from a non-US source?
Actually, none of that may matter. Assuming you bought the device new some 5-6 years ago (I'm uncertain when the Roku 2 was discontinued overseas), it should still perform well. The Streaming Stick+ (the new device, model 3810) having the same issue, and since it doesn't use an HDMI cable but plugs directly into the TV, seems to rule out everything except the TV.
Still, that's weird that two separate TVs would develop the same issue. Struggling to find something in common -- separate Roku, even separate Roku models, separate HDMI connections -- the only thing that comes to mind may some external force that's impacted the TVs. Power failures? A common user making changes to TV settings? I'm grasping here.
I'm not sure what to offer. This may take some pondering.
Roku Community Streaming Expert
Note: I am not a Roku employee.
If this post solves your problem please help others find this answer and click "Accept as Solution."