There are plenty of alternative phrases and synonyms that can be used to convey the meaning of "grow tired". Some of these include: become exhausted, wear down, tire out, fatigue, run out of energy, languish, wilt, droop, lose steam, succumb to fatigue, and flag. Each of these phrases can effectively convey the idea of becoming tired or worn out, but may be able to add some variety to your writing or speech. Whether you're describing physical or mental exhaustion, these alternatives can help you express yourself more clearly and in a more interesting way.