Almost definately clutch band that has been burning away. The reason you have had trouble getting it to engage is most likely that stuff is plugging the valves and interal lines and the pump. Trans oil pressure is lost and it starts to act up with the shifts.
Some have been able to extend the inevitable failure by having the trans flushed, or there are some products that can help. But like R Leo said, time to start budgeting for a new tranny.