Is a EULA required for each software update?
Although there might be case law in some jurisdictions answering in the affirmative, the issue ought to be assessed from the principle of contract law that parties to a [cognizable] contract enter its conditions knowingly and willfully. Thus, the questions would be: Does the sole act of installing an update justify the presumption that the parties' rights and duties have automatically changed? And, if so, what new conditions can a reasonable person identify in the absence of update's EULA?
As a precaution, EULA may preemptively make it clear that its terms, unless indicated otherwise in a subsequent update, are applicable also to updates of the product.
Especially where an update is to be construed as continuation of a service/product that had been agreed upon, an allegation akin to "the update in and of itself changes the parties' rights and duties" seems devoid of merit. However, the approach mentioned in the preceding paragraph would overcome legal precedents (unforeseeable or otherwise) holding that an update inherently strikes any previous EULA.