Has it ever fruited? If so, it's normal for it to die. If not, you may have been overwatering and it may have root rot. I water mine only if it doesn't rain for 3 days. I usually have dying leaves in the summer during heavy rains, though.

It has never fruited. This was a pup that came up from the ground after last January's freeze.

It is in a spot near where water runs off of the garage roof, so when it rains it gets a lot of water. But I thought that bananas love lots of water.

John

They love water, but nothing likes wet feet all the time. They are prone to root rot. Maybe you should move it.

"Banana plants are not flood tolerant. In general, plants may survive 24 to 48 hours of flooding caused by moving water. Stagnant water kills plants quickly. Bananas should not be planted in flood-prone areas. In areas where the water table is high and/or frequent soil saturation or very brief flooding occurs, planting on beds is recommended. Symptoms of continuously wet but not flooded soil conditions include plant stunting, leaf yellowing, and reduced yields. "

Here is a link that might be useful: University of Florida: Banana Growing in the Florida Home Landscape

I think you nailed it.
Thanks,
John

Phosphorus deficiency