I am a retired guy learning how to weld and tinker on hobby farm. Just picked up a used 7 inch King horizontal saw. It looked like new except for it being covered in shavings and garbage end cuts. I didn't know where to start, now I do. I am excited to clean it as new and use the cooling system properly before my first cut. Knowledge of the band selection/speeds will be the next learning curve. Luckily there was some junk angle iron still in the vise, so I'll play with something similar to match. Your videos on basic welding are luring me next. You are a good teacher. Even Millennials would pay attention and learn from your full explanation.
Generally, when a balde comes off the idler wheel or drive wheel it is down to two things. Incorrect blade tracking or the bearing's in either or both wheels have worn. I would try setting the blade square in the horizontal and vertical planes, check the distance between the blade guides is set for the matrial you are cutting and make sure the blade is running on and spinning the blade guide bearings. My 7x12 saw has six blade guide bearings and all six need to be working and set correctly.