I just wanted to provide some feedback for anyone else who might encounter this problem.
Earlier today, I did a hard reset and initiated a restore-from-backup. When prompted for email account passwords, I only entered one for the corporate exchange account and left the others. Once the initial sync was complete, I went in and found the "as item arrives" there again, and happily switched to it.
However, after going back and filling in the passowrds for all other 8 or so email accounts I have, I discovered that one of my GMail accounts did not have the "as item arrives" while 3 of my other GMail accounts did! I deleted the offending GMail account then re-added it. Didn't do anything.
THEN, I deleted the offending GMail (call it "account A") account AND one more GMail account (call it "account B"), where the "as item arrives" option was present.
I soft-reset the phone, re-added the "account A" GMail account first and lo-and-behold, the "as item arrives" option was back. HOWEVER, "account B" which originally had the option, no longer did when I re-added it next.
This leads me to believe that there is a limit to the number of email accounts that can be set to "as item arrives." I'm thinking it's the first 5 that try to adjust the frequency of email synchronizations.
So that's my story. Hope it helps someone else