There are two types of soaps: hard (such as Williams) and soft (like ClassicShaving).

I use the same method with soap myself. Soft soaps don't tolerate this very well. Mine lasted about a month as well. A cake of Williams lasts a whole lot longer.

What you might try is use a second mug for hot water only. Soak the brush while showering, then drain the brush and whip up later. I believe, although I have not confirmed, you should get better life out of your soap. I haven't tried this, as I bought some Vulfix cream at the same time, and it makes nice lather, smells good, and lasts forever.