WP 3.2 "Database Update Required" Keeps Reappearing

Hello,

I upgraded to WordPress 3.2 about a week ago. Everything seemed to be working ok, but in the last two-three days, I’ve been getting the following message two or three times per day:

Database Update Required
WordPress has been updated! Before we send you on your way, we have to update your database to the newest version.
The update process may take a little while, so please be patient.

Note: that only happens (very sporadically) when I try to open a new page on the admin panel — any new page: comments, new post, tools, etc.

The update process takes one second. Either things go back to normal after that or… the admin panel switches back to the old version of WordPress and tells me I need to update to WP 3.2!! That goes away after I refresh the screen or WP forces me to reupdate the database AGAIN…

The vast majority of the time, WP 3.2 works flawlessly, so why those hiccups two/three times per day — and only since last Friday or Saturday? Are others having the same problem? How can this be fixed?

I just did a forum search, including the WP 3.2 thread, but found nothing on this issue. [Addendum: Actually I did find a few threads, but none regarding this particular issue I’m having with WP 3.2.]

Any assistance would be much appreciated.