Just tried rebuilding. Didn't fix the problem.
Not sure about the original poster, but I have an IMAP account with "Keep copies of messages for offline viewing" disabled. (For security reasons.) I also did a clean install of Lion, so Mail's "previous recipients" list is presumably empty. Not sure if doing any of these three things differently would solve the problem. ButI have good reasons for my current setup. So I guess I'll be dropping Apple Mail too, if this doesn't get solved.
Under Snow Leopard, I could search info in the mail headers (sender, recipient, subject), but not stuff in the message body (since, unlike the headers, the full messages weren't on my hard drive). I'm pretty sure I could search for recipients, even if I hadn't ever sent them a message using Apple Mail. Under Lion, the same functionality seems to be present. But I can only access it after I've sent a message to somebody once using my current Apple Mail installation. After that, their name shows up as a suggestion when I start to search for it, and when I select it, I can see all of the messages they've ever sent me. But until I send them a message for the first time using this copy of Apple Mail, their name will never be suggested,and my search will turn up blank, even if I can see several messages from themin the first screen of my inbox. Weird. Seems like the "name suggestions" feature of search relies on Apple Mail's internal list of previous recipients. (Sort of like the "name suggestion" feature when you were typing in a recipient's e-mail address always did.) This is unfortunate, as it's now the gatekeeper to header-based searches. (Or at least for searching the "sender" field. Doesn't seem to be any way for me to search the "subject" or "recipients" fields anymore.)
If this problem is in fact limited to people who have "keep messages for offline viewing" disabled, then I suspect this may be another case of Apple not really caring about people who do things differently than the way Steve Jobs intended.