Texas Local Government Code - LOC GOV'T § 22.041. Vacancy on Governing Body is Created

(a) If an alderman moves from the ward from which the alderman is elected, the alderman's office is considered vacant.

(b) If a member of the governing body is absent for three regular consecutive meetings, the member's office is considered vacant unless the member is sick or has first obtained a leave of absence at a regular meeting.

(c) In addition to an absence described by Subsection (b), a member of a governing body is also considered absent for the purposes of that subsection if the member is not present at the adjournment of a meeting at which a quorum is established, unless the member is first allowed to withdraw by the unanimous vote of the members present. This subsection applies only to a municipality that is located in a county that borders the United Mexican States and contains a municipality with a population of 500,000 or more .