Rrgh, sorry yet again.
Could you try this?
1. Make an edit in TaskPaper-iOS
2. Tap the document's title and select "Sync All Now"
3. Once it's finished, head over to Dropbox's website and check the events page (https://www.dropbox.com/events). Does the sync event show up there?
If so, then running in reverse, does switching to another document and then back again create a second sync event? If the document is all synced up properly, then it shouldn't (until you make another edit).
One way I can reproduce this on my end is to make sure I'm on a very slow network (spotty 3G, for example, or use a network conditioner to artificially slow down my connection), open the app, and then make several edits without closing the keyboard before sync has finished (with external changes needing to be synced in and not given the chance to do so).
Another way to check to see if sync the culprit or not: Turn off automatic sync from the Dropbox settings page, and then see if edits are being lost between document switches.
I'd also recommend a delete/reinstall just in case… that shakes out any issues caused by bad updates over time. A general measure, but surprisingly reliable. Sorry if that was mentioned anywhere before.