I finally googled online to see if my problem is unique. Lo and behold, I'm not the only one having the exact same problem! Surprised? Not. Turns out Apple recently made a change to Notes so that it will silently sync whatever notes being edited with the user's online email! True enough, unbeknownst to me, there is a "Notes" folder created for each of the email accounts (I had two) I set up on my iPhone.
That sure explained why something is seemingly overwriting my texts. Depending on the time the sync occurs and the speed of the data transfer, if I happen to be editing during the syncing, the service replaces the version I'm modifying with an earlier cached version!
Good news is there's an easy way to stop this from happening again. To turn off sync for Notes, on the phone, go to Settings > Mail, Contact, Calendars > Mail Account and make sure the Notes is on Off position. Also in iTunes, click the info pane and deselect the option to Sync Notes. Phew!
When Notes is turned off under the email account setting on your iPhone, you may notice some of the notes you saved before missing. This is because when syncing occurred, those notes entries are filed under different folders, depending on which email account the notes are synced to. There are two ways to get them back, both are cumbersome. You can either copy the note from your email or from the old entry on Notes--to get access to it, you need to turn the Notes under your email setting(s) back on so you can see the corresponding folder(s) under the Notes app, then turn the Notes syncing back off, and paste the note into a new entry in Notes. *sigh*