I'm cruising through here looking for a different problem with ArcPad 8, however, I have seen this problem before and I'll tell you what we found.
We are checking data out of, and back into SDE versioned geodatabase feature class and hit the same error.
What we found was that the connection properties dialog box in catalog shows us to be connecting from our DEFAULT database and not the version that was created just for field editing. (This even though the Source display tab shows us to be editing the correct version.)
By changing the "Connection Properties" / "Connection details" / transactional version to a public version created for this purpose. and then checked data out and into that version only. We no longer received the error messages.
Any data that was created or modified while using the wrong version had to be extracted to a shapefile using ArcPad Studio, and then jump through a few hoops with "Load Data" tool to get it into the correct SDE feature class version.
Basic advice: Review your source data connection and your checkin connection are the same.
TIP: When you are ready to check out or in, click on the !Version Manager! button and make sure you are not using public or protected version.