Correct Japanese — but it's a full sentence, and Japanese has better ways to say this.

What a Japanese person actually thinks
Reads as dialogue, not as an inscription. Seven characters with four hiragana — it looks like a line from a script rather than something carved.

Meaning

Literally: never + will not give up
Actually: 'I will never give up.' Grammatically perfect and completely natural as speech.

Scores

Naturalness●●●●●

Entirely natural Japanese. The problem is register, not correctness.

Coolness●●●●●

Long and script-mixed. Japanese has centuries of compressed four-character idioms for exactly this sentiment — using a spoken sentence instead wastes them.

Watch out

lowSeven characters is a lot of real estate, and the hiragana will be the first thing to blur.

Get this instead

百折不撓 hyakusetsu futō
broken a hundred times, still unbent

The same statement, compressed into four dense kanji with a classical pedigree.
不撓不屈 futō fukutsu
indomitable

The most common four-character version. Formal, forceful, no hiragana.

On skin

決して諦めない

Orientation: vertical

Mincho if you keep it — but consider the four-character options first.