For my top choice school, I sent a LOCI about every 3-4 weeks, each letter highlighting in detail a specific aspect of the school or a particular program that I thought I could contribute to and why I liked that program/characteristic of the school. I also reiterated in each letter that I would unquestionably attend if admitted. As far as timing goes, I sent my very last one so that it would arrive at the school and be read just before or around the deposit deadline, so that when it was time for them to admit people off the waitlist, my name would be fresh in their minds. I figured that they would be looking at the waitlist as soon as possible after they knew what the class was going to look like so that they could get going on filling up the class. I was admitted to my top choice during the first round of admits that they did off the waitlist, so I guess I did something right. (The extra letter of recommendation probably helped too).
For another school, I wrote a nice LOCI right after I was waitlisted and then was admitted a couple months later without sending any other LOCIs, so I guess it really depends on the school. I feel that for this second school, I probably could have sent maybe one more LOCI, but obviously it wasn't necessary.