Some artists take longer than others. There's weekly and monthly manga publications & Azuma Kiyohiko works for the latter.
He also does the merchandise and will often revise and expand chapters after they've been published in the magazine Dengeki Daioh for the collected editions.
As for why Yotsubato chapters come out sporadically, here's some guesses-
-He's been doing manga for more than 20 years and is in his 50's.
-He's a perfectionist and doing gentle, humorous, slice of life stories with detailed backgrounds takes a while to do.
If it takes him 2 days to do a page, plus art for merchandise, outside commissions (like the Wonderfest posters he does), revising chapters for the collected editions plus painting covers for them and the time he puts into the Yotuba merchandising company Yotuba Sutaizo, you can see why he might not be able to put out chapters regularly (even with the help of background art assistants) http://www.yotuba.com/
Currently he's over half way done with Yotsuba& vol. 15 and he started the series 16 years ago, so it's averaged out to almost 1 volume a year.
I do think he went through a few periods where he took time off from the series.