Question: After the Appleseed Cast grew to fame and toured with Frank Black, how many times did they break up?

Context paragraphs:
Old Canes: Old Canes is a rock band from Lawrence, Kansas currently composed of front man Christopher Crisci (of The Appleseed Cast) on vocals and guitar, and a rotating cast of musicians.  Because most of the band members, including Crisci, participate in other bands, Old Canes is joined on tour by other available musicians known to the band, including John Momberg (of The Appleseed Cast), Taylor Holenbeck, Sam Goodell, Rusty Scott, Kelly Hangauer (of Fourth Of July), Lucas Oswald (Minus Story) and Jeff Stolz, in what they call a "musical collective."  Past members include Nathan Richardson (Casket Lottery), Jordan Geiger (Minus Story), Eric Verhar, Tyler French (Minus Story), Gabriel Booth, Kelsey Richardson, and Jon Anderson (Boys Life).

Frank Black and the Catholics (album): Frank Black and the Catholics was the debut album from Frank Black and the Catholics.  The backing group on this album performed on Black's previous album, "The Cult of Ray", but the group name was first adopted on this release.  The album was recorded live to two-track tape over the course of two days in 1997, but a protracted dispute with Black's label American Recordings, reportedly over the "raw" sound of the recordings, delayed its release for 18 months.  The album was released in June 1998 in the MP3 format on GoodNoise.com (precursor to eMusic) and was the first album by a major artist to be commercially released on the Internet.  The album was then released in the fall of 1998 by SpinART records in the US.  During the interim, Lyle Workman left the group and was replaced by Rich Gilbert, and Black prepared the follow-up, "Pistolero".

Tijuana Crime Scene: Tijuana Crime Scene was a short-lived supergroup featuring members of Spoon, Hot Rod Circuit, The Golden Republic, The Anniversary and The Appleseed Cast.  Formed in 2000, they released an EP and toured briefly with Frank Black before splitting up in 2003 due to the busy schedules of their respective music careers.

Graveface Records: Graveface Records is an American independent record label from Savannah, Georgia, solely owned and operated by Ryan Graveface (who plays in the groups Black Moth Super Rainbow, Dreamend, the Marshmallow Ghosts and the Casket Girls).  He has released recordings by Serengeti, Dosh, The Appleseed Cast, Haley Bonar, Xiu Xiu, Monster Movie, Dreamend, Jakob, Jason Molina, Mount Eerie, The Loose Salute, the Lava Children, Black Moth Super Rainbow, The Seven Fields of Aphelion, and Whirr.

Low Level Owl: Low Level Owl can refer to either of two albums by The Appleseed Cast:

Frank Black Francis: Frank Black Francis is a 2-CD set released in 2004 by Frank Black, roughly coinciding with the Pixies reunion tour.  Disc 1 consists of a March 1987 solo acoustic demo tape recorded by engineer Gary Smith, just prior to the first Pixies recording session.  Disc 2 is a contemporary recording of Frank Black reworking a number of Pixies songs with Keith Moliné and Andy Diagram, who are part of David Thomas and Two Pale Boys.

Black Francis: Charles Michael Kittridge Thompson IV (born April 6, 1965) is an American singer, songwriter and guitarist.  He is best known as the frontman of the influential alternative rock band Pixies, with whom he performs under the stage name Black Francis.  Following the band's breakup in 1993, he embarked on a solo career under the name Frank Black.  After releasing two albums with record label 4AD and one with American Recordings, he left the label and formed a new band, Frank Black and the Catholics.  He re-adopted the name Black Francis in 2007.

The Evpatoria Report: The Evpatoria Report is a Swiss post-rock band.  The band was formed in January 2002, and it consists of two guitarists, a bassist, a drummer, and a violinist/keyboardist.  The Evpatoria Report have played concerts in Paris and toured throughout Switzerland, playing with bands such as Red Sparowes, The Appleseed Cast, and Mono.  The band was on a hiatus from 2008 until they announced their return to the studio in April 2015.

Frank Black 93–03: Frank Black 93–03 is a compilation by Frank Black.  It highlights the 10 years of his solo career after disbanding the influential alternative rock band, the Pixies in 1993, as well as songs from the many albums he created with backing band "the Catholics".  Included also is material from his next solo album, "Bluefinger", in the form of a hidden track, "Threshold Apprehension".  Each release comes with a second disc of live recordings, which varies depending on the region the album was released in.

The Appleseed Cast: The Appleseed Cast is an American rock band, based in Lawrence, Kansas, with 20 years of recording and touring.  The band was founded in the early days of emo by singer-guitarist Christopher Crisci and guitarist Aaron Pillar, and quickly grew to fame.  The Appleseed Cast has steadily evolved over the release of eight full-length albums with Crisci at the songwriting helm, changing lineups but never breaking up, continuing to hone the TAC sound.  The band’s current lineup includes Crisci, Taylor Holenbeck and Nathan Wilder, and touring musicians Ben Kimball and Nick Fredrickson, among others.

Supporting paragraphs: Tijuana Crime Scene The Appleseed Cast
Answer: never breaking up