I just want to mention that the 4 lives thing isn't true. I started the level with 2 lives, died twice in the pit, and when I had zero lives left the pod showed up. Just thought I would clear that up.
So it should only take four loops where you go from the start of the stage to where the capsule is. You have to "enter" the stage to start each new loop. "Entering" the stage is when you see the "Ready" words flashing on screen while you teleport into the stage. This can be done either from dying or from using the Escape Unit to get back to the Stage Select then selecting the Fortress stage again. On your fourth run, you have to have full health before you drop down to where the capsule is. If you don't have full health, it won't spawn.
Basically, it's the same conditions you needed to spawn the Hadouken capsule in Mega Man X1.