Does this plant become root bound real easy? If so, will it kill the plant?

I believe it can. Probably just about anything will eventually become root-bound, then you just need to re-pot it. The signs I am aware of that a plant might be root-bound are the leaves around the lower part and outer edges begin to look wilty and the color will be off.

Wilty. It's a new word I just came up with.

Being this is an annual, tropical perennial, I am assuming (oops, shouldn't do that) you are using it as an indoor plant. Right?

Yes, it's an indoor plant or a full shade plant. I enjoy him on my patio.

I have noticed the leaves are falling off. Time to re pot! Thanks for the information.