(CNN) -- A Texas judge denied the appeal of fundamentalist sect leader Warren Jeffs on Thursday, the same day a jury considered testimony to determine how to sentence a key figure in his church after his own bigamy conviction.
The leader of the Fundamentalist Church of Jesus Christ of Latter-day Saints, Jeffs is serving a life-plus-20-year term in Texas for sexual assault. He was convicted in August of the aggravated sexual assaults of a 12-year-old girl and a 15-year-old girl, who Jeffs had claimed were his "spiritual wives."
On Thursday, Chief Justice J. Woodfin Jones of Texas' Third District Court of Appeals ruled against Jeffs' appeal of that conviction.
In his ruling, Jones noted Jeffs, who represented himself during part of his trial, missed several deadlines related to his appeal. Specifically, he did not file "a written designation specifying the matters to be included in the clerk's record nor (make) arrangements for payment of the record with the clerk's office."
"We informed Jeffs that his appeal may be dismissed for want of prosecution if he did not make arrangements for payment of the record and submit a status report regarding this appeal on or before January 23, 2012," Jones wrote. "To date, Jeffs has not responded."
The 10,000-member church that Jeffs heads is a breakaway Mormon sect that openly practices polygamy in the twin border towns of Hildale, Utah, and Colorado City, Arizona, as well as on its Yearning for Zion ranch near Eldorado, Texas. The mainstream Mormon church renounced polygamy more than a century ago.
Many sect members have disavowed Jeffs in light of his criminal convictions, while others are defending him and calling his conviction on sexual assault charges an act of persecution.
Meanwhile, the man who temporarily replaced Jeffs as business head of the church, Wendell Nielsen, was in a Midland, Texas, court on Thursday for the punishment phase of his own trial.
Nielsen was convicted Wednesday on three counts of bigamy, according to Lauren Bean, a spokeswoman for Texas Attorney General Greg Abbott.
"It's a fabulous win for the victims of polygamy that he was convicted on these charges," Flora Jessop, who fled Fundamentalist Church of Jesus Christ of Latter-day Saints as a teenager, told HLN's Dr. Drew Pinsky.
Testimony was offered, but there was no sentence decided upon by late Thursday afternoon, Bean said.
While awaiting trial in February 2011, Jeffs regained control of the sect and ousted at least 45 high-ranking members considered a threat to his leadership, two well-placed sources told CNN.
In that reshuffling, Nielsen was replaced as the church's business figure as Jeffs had signed documents retaking control, according to the sources.
CNN's Gary Tuchman contributed to this report.