Your probably over-extending with an arched back when doing bukiwaza. Not an unusual bad habit amongst Iwama-stylists. Try to slow down the weapons and focus on form and forget about power for a while.
With regards to weapons, and especially the jo, I have come to notice that over-extension (forward) can definitely put a strain on the lower back, but in general it seems hard to put proper extension (sensei and sempai always talk about the importance of extension with weapons) in the suburi without tightening/clenching/compressing the back. How can one do both things at once?
Also, in general, my observation of yudansha who have been around the block is that back pains--especially lower back--are quite common.