One of the reasons I used to get a stiff lower back is that I was always leading with the hips and although i thought I was upright, I was actually leaning back and this was putting strain on my back. Once I had corrected the problem it went away.
My advice is to go and see a chiropractor/osteopath if it continues. I saw one after landing on my head once and they were great - I felt immediate relief. Often they can determine the cause of the problem which may not be aikido related at all.