Have you tried power cycling your LCD on/off when it does it? Does that 'fix' the issue also?
If you can reinsert the RGB cable and it fixes the problem sounds more like an LCD issue than an Amiga issue. Have you got a scandoubler in your setup somewhere or does your LCD sync to Amiga screenmodes natively? I'm not an expert by any means but it sounds like your LCD loses sync with the Amiga after a certain period of time although why that may be is beyond my knowledge. Reinserting the RGB cable sounds like it's causing the LCD to re-sync successfully again.
Have you got another Amiga you can try on the same LCD? That may point the finger in the appropriate direction more accurately.
