I got the pipe from the dragon area. I got turned around later in the game and went back to an early saved game. I got the pipe again, but now i can't get out. The gate is locked. I have replayed several times, but the gate is always locked. I can't use an F-Link to get out, and dynamite does not work. I do not understand why I did not have this problem the first time, but now every time I replay the gate is locked. Is something required that I did the first time that i am not doing now?

There are a couple of stone buttons located all around the area that you have to press. Just run along the edge of the pit and look for them and jump on all of them to get the gate to open.

I found out what the problem is: I broke the game. Now as often as not, I cannot even get in. The gate is closed. It is quite random. I guess that I replayed the sequence too often.

If I'm not thinking about the wrong part of the game, I think the problem occurs when you load a savegame after you entered the arena. When you first enter the arena the gate gets locked behind you and the Achondar appears. If you load a savegame after that, the game apparently doesn't remember to reset the gates, so they are instantly locked again, even if you hadn't entered the arena when you first saved.
But, I could get around this by restarting the game and then loading a savegame from before I first entered the arena.

If you get stuck in the Achondar's lair and don't want to reload back to an earlier save, it is possible to jump out using the rocks on the inside of the walls - you just need to find a spot where Cutter can stand on the rock long enough to jump up and grab the wall.