From what I can find it appears you are not alone.
There is a setting to "save sent messages to send folder" that you need checked but some have stated they do have that on and they still disappear.
Another person said they used the Repair feature on the Office DVD and it fixed the problem (you should be able to initiate this from Control Panel\All Control Panel Items\Programs and Features as well though it will still likely ask you to install the DVD)
Someone else said it seems to work for their pop3 accounts but not their imap accounts and the reply to that was that there is a different setting for imap accounts (example Google). If you have this type account then you likely need to have "sent items" enabled within the internet account and then set up outlook to point to that online sent folder.
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Another person said "I am using Outlook 2010 in "Conversation View" which is great except for the fact that Sent Items do not show up in this view." and they came back and answered that "It turns out that you need to have your mail indexed via Instant Search for this feature to work. I had that feature turned on, but I did NOT have "Cached Exchange Mode" turned on, which meant my mail wasn't actually being indexed. Now that I have cached mode turned on, I can see my send items in my conversations"
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