Is the Latin word vivere (to live) cognate to the Hebrew word aviv אביב (Spring)? Someone pointed out the resemblance to me, and it looks plausible, but I haven't found any conclusive answer.
Arnaud Fournet's answer is correct: there's no evidence for a relationship. But to add a bit more evidence that there isn't a connection…
The Classical pronunciation of vīvere was something like
/wiːwɛrɛ/, while the Biblical pronunciation of אָבִיב was something like
/ʔɑːbiːb/. Both words are attested well before the relevant sound changes (W-hardening and beghadkephath spirantization) made them look similar.
In addition, אָבִיב is a regular formation in Hebrew. The pattern קָטִיל (_ā_ī_) is fairly well-attested in Hebrew for periods of time, and the root אבב ('-b-b) for "beginning to grow" is attested in both Hebrew and Aramaic. It's very unlikely that a loanword would fit so nicely into the Semitic root system.
Finally, vivere is a regular formation in Latin. It comes from the well-attested Indo-European root *gʷ-yh₃-, with cognates in Germanic, Indo-Aryan, Hellenic, Slavic, and Celtic at least. This pretty conclusively rules out a loan into Latin.
EDIT: To drive the last nail into the coffin, Nadav Har'El has brought up Amharic አበባ (abäba), from the same Semitic root. This shows that the '-b-b root is significantly older than the Latin language itself. There could still have been some contact between an older stage of IE and an older stage of Semitic, but as you've seen, the underlying IE and Semitic roots don't look anything alike; their descendants have converged by chance.