You were denied. Read the statute again.
A chief appraiser who denies an exemption must deliver written notice of the denial. You then have until the later of May 15 or 30 days after the notice to protest it to the Appraisal Review Board — and a protest of a denied exemption is heard on its merits, not on whether you filed on time.
Tex. Tax Code §11.45; §41.44
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Your protest route
Protest the denial to the Appraisal Review Board. The deadline is the later of May 15 or 30 days after the notice was delivered. A protest of a denied exemption is heard on the merits of your eligibility, so bring the VA letter and the statute rather than an argument about process.
Texas requires the chief appraiser to give you written notice of a denial, but unlike some states it does not prescribe what that notice must contain — so there is no "the letter is defective on its face" argument to make here. What Texas gives you instead is a strong protest route, and a statute whose own words are often the answer.
One more thing worth checking
The most common wrong denial in Texas is a refusal of the total exemption because a veteran's combined rating is below 100 percent, where that veteran holds a determination of individual unemployability. §11.131(b) entitles a veteran who receives 100 percent disability compensation "and a rating of 100 percent disabled or of individual unemployability" to the total exemption. Those last four words are in the statute. Ask the district to read subsection (b).
Read the record on §11.131