The rule is not always clear on postponements. I have changed the practice area to criminal to see if someone practicing that might tell you what criminal courts generally do.
This is not legal advice. You should always discuss the specifics of your issue in person with an attorney. Be aware that there are time limits on all claims that depend on the kind of claim, so do not delay in seeking an attorney.
Did you appear on the first court date and get sworn in? If so, you'll have to appear whenever instructed by the court or DA. If not, they have to issue a new subpoena.
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Ms. Jaggers answer is how I have seen things done in Texas state courts for almost 30 years.
Answers on Avvo are for general information purposes only and should not be relied upon as legal advice. No attorney / client relationship is created by providing this answer. For specific advice about your situation, you should consult a competent attorney of your choosing.