In my last district, we were on 9 week periods. The UIL C&CR is hard and fast about a grade check at the end of the first six weeks of school, so that one happens regardless (because FOOTBALL!) but it gave a TON of flexibility for the rest of the year.
Our district's interpretation, backed up by Rule as Written on the UIL site, was that if a kid passed a REPORT CARD they were eligible for the entire next reporting period, full stop.
That meant that if a kid passed Week 9's report card, they were eligible until the second semester. If they passed the second nine weeks, they were eligible until basically Spring Break. And if they passed that last one, they were/are eligible for the rest of the school year.
Since UIL fell for me in the first week of March, I stressed passing the 2nd 9 weeks, and had nearly 95% of my kids eligible every year because of this. The kids that weren't passing had TWO progress reports in which to try to reclaim eligibility. I could focus just on those two or three kids who were failing to get their grades up by the third week - and they were good for the rest of the period.
Until UIL and the legislature pulls its collective head out of its cloaca, we're stuck with NP/NP. As we are, a 9 weeks cycle is MUCH more conducive to retaining student athletes and musicians than a 6 week one.
All that being said, this was before the NP/NP restriction for C&SR was revised. This applies to IF your program is held accountable to NP/NP for Spring UIL.
If not, I think I'd rather be on 6 weeks. Most marching seasons are about 12 weeks long from first game to last (about a third of Texas schools make the playoffs, and half of those lose in the first round, and the regular season is 11 weeks long). You're going to have two grade checks that count in that time. Do you want them in the sixth and EIGHTH week (since many schools set their first "nine weeks" as only eight weeks long because of uneven semesters caused by Christmas) or the sixth and TWELFTH week?