My guess for the streaked ones:
It is more of a rendering problem due to the games far-background. Since the game does not render anything new in that area it simply streaks w/e passes over it.
In most cases it should not be a problem but in elgas / lavalons case something must of went wrong in losing the should-be background.
That is not the reason. A so-called backbuffer usually consists of a Color Render Target and a Z-Buffer. In cases that the developer can assume that everything is rendered every frame the Color Render Target is not cleared every frame only the Z-Buffer. The Z-Buffer is the buffer which saves the depth of each 3D object to make sure that things which would appear in the back of other things already rendered are not rendered.
A game usually renders all objects in a frame (which is the case for all rendering frames in Dragon Saga) and therefore it's only needed to clear the Z-Buffer not the Color Target. In case that things can't be rendered which are expected to be rendered and the Color Buffer is not cleared the effect you see appears which is called "Hall of Mirrors Effect".
VRAM: 1 GB
This is quite less. The specifications for the game are a bit outdated.
Still none of the posted configurations are giving a real explanation why this happens.
Usually this problem begins to happen if RAM or VRAM is full and the game can't allocate needed memory. Another problem often is corrupted texture/model files but this can only be the case when these problems are appearing immediately and not after some time.
Still the "explanation" why it happens after some time can only be that the game is not able to get enough memory for the textures/models or fails to create them because of any other reason.
Since everyone posts their specifications I want to post my testing specs as well (which are not causing any problems):
AMD Phenom II x4 965 - 8 GB RAM - AMD Radeon 6850, 2GB VRAM - Windows Vista, Windows 7
AMD FX 6850 - 8 GB RAM - AMD Radeon 7870, 2 GB VRAM - Windows 7
AMD Ryzen 1600x - 16 GB RAM - nVidia GeForce GTX 1060, 6 GB VRAM - Windows 10
I will continue investigating this issue but finding the problem is not easy if it does not occur on any of my testing systems.