The flame does not burn right on the end of the pilot. Eventually the pilot goes out because it is not burning right on the end.

Ventless gas heaters can be a dangerous item especially if being serviced by someone who has not received the specific training for the unit being worked on. Usually they consist of a pilot, thermocouple and most important an oxygen depletion sensor. The pilot is probably going out because of a problem with the oxygen depletion sensor OR the pilot orifice is restricted. I do not suggest trying to repair the unit unless you are trained to do so or you have a factory repair manual for the item and read and understood exactly what you are working on.