A potted plant will run out of nutrients and has no way of getting them unless you provide them in the way of fertilizer. Is there a reason why you don't plan on fertilizing? The accepted advice is not to overfertilize as it will sacrifice flowers in favor of leaves, but they do need fertilizer.
htop said she's had a miniature (not dwarf) crepe myrtle for three years, and it's only about 5 inches tall. Here's the link she posted, perhaps they have some info for you about care and feeding of small crepes in containers:
I found a website that straightened the crape, crepe name for me. The trees as a group are called crape. The Natchez group of crapes are called crepe. I hadn't paid much attention to the spelling before.
I did not order my mini crepe myrtle from this place. I am sorry that I posted a link to the website. I can't remember for sure where I bought it, but I think I got it from Rainbow Gardens Nursery here in San Antonio.
Maggie, I think Susie bought one just like the one I have. I wasn't sure because it (and mine) are not in bloom yet. I was up bright and early today and just had to peruse what was happening at DG before I started my yardwork.