If your mint plant has been producing flowers (usually a cone shaped inflorescence), then it has started bolting. While mints are perennials and I haven't known them to die off quickly after bolting, it sure is a process that makes the plant focus its resources elsewhere (flowers). You should take them out as soon as they appear.
I have known my basil, cilantro and parsley plants to start growing woody stems when they're in an advanced stage of bolting and I'm quite sure that it is also the case for mint.
A plant is said to be root bound when it is grown in a container too small for it. The roots fill up the volume of the container and when it cannot grow any more, the plant stops growing too. A root bound plant will not grow even if the conditions are favourable and you have a perfect watering/feeding/fertilizing schedule. Here's how the roots will look like inside the container.
Source: Virginia cooperative extension
The article linked above puts it quite well:
At what point do plants stop growing in a pot? It's a bit involved, but the simple answer is that new growth stops or slows when they become rootbound. So what's rootbound? Rootbound is when there is no effective space for new roots to occupy. Roots effectively occupy the entire volume of space between the soil particles. One of the first symptoms of being rootbound is, in fact, that plant growth slows despite favorable environmental conditions (light, water, fertilizer, etc). The second symptom is that rootbound plants begin having difficulty taking up fertilizer. This is undoubtedly related to the inability to form new root tissue. You see this as a chlorosis despite the fact that they have been properly fertilized.
Given that you grew it in a pot specifically to contain the roots, I'm quite certain that this is the problem. You could try transplanting it to a bigger container to provide more space for the roots. Don't forget to untangle the bound roots before you transplant.