Ventless fireplaces are good for about 4-6 hours of continuous use. They usually burn propane instead of regular gas because it burns cleaner, but that's not always the rule.
They need to burn clean because they "vent" inside the room. In other words, the exhaust product, gas, CO2, or whatever, vents into the room where the fireplace is situated.
Although they burn clean by themselves, they have a nasty habit of taking in room air for combustion, along with everything floating in that air. From dust particles to aerosol sprays, to carpet fibers, they get sucked into the fireplace, then burned. Whatever toxins these materials emit when this happens, are then released back inside the home. This is another reason not to let them burn too long.
Although I would not call them dangerous, it can be a particular concern in really air-tight homes, or for people with allergies. I learned all this because my wife has such an affliction. She even has problems with regular wood-burning units. For this reason a direct-vent fireplace can be a good alternative since the fumes are vented outside, and no real chimney is necessary, only a direct vent outside. You may be able to convert your unit if you feel the need.