Yes and no.
Yes - there appears to be a feature where the messages app will not initially draw older messages based on some combination of time and activity where it used to show everything more reliably.
No - In all cases I've seen, messages are not deleted due to this feature so it's hard to know why your "load more" button is displayed, but doesn't actually retrieve more messages.
For example, I have SMS and iMessage conversations that exist in the app from 2010 and 2011. Some conversations started as SMS and moved to iMessage in October 2011 and haven't been shortened with the "load more messages".
From my usage - all of the older conversations that are not more than 10 or 20 items in the history are all presented perfectly on iOS 5. Only conversations (both SMS and iMessage) with more than 30 or so messages have the display shortened and the option to ask for more messages to be loaded on demand.
I'm fairly certain that all the messages are still stored - just not rendered and taking space on the view until you ask for more content.
I have never had a problem with iMessage deleting messages on me due to no space or other considerations - but I do use PhoneView to periodically archive both my messages and other contents (voicemail, call history) to a Mac since keeping this history is something I prefer to have.
I was searching for information on this myself because I needed to back up my email data from the device before doing a restore (it's just shameful that Apple doesn't consider your email messages to be important enough to include in its backups). The following information is valid for IOS 6, I hope it applies to your situation with IOS 3 as well. On IOS 6 at least, you won't need to mess around with SQlite or anything, it's all plain text.
You need access to the filesystem on the device. There are various PC and Mac apps that will browse the files on the device -- Ifunbox is one that claims to allow access to the filesystem without jailbreaking.
Instructions for jailbreaking your specific device (if it turns out you need it) can be found at http://stateofjailbreak.com/guide/iphone-3gs/3-1-2/.
The emails are stored in User/Library/Mail (that's a symlink, the actual path seems to be var/mobile/library/mail). Just copy the whole thing to your laptop.
Inside there, you'll find directories named after each email account set up on the device. There's a pretty self-explanatory folder structure within each account folder. Once you drill down, the emails themselves are stored in individual plaintext *.emlx files, complete with all headers and uuencoded attachments (there's also sometimes an "attachments" folder which has the extracted version of the attachments). On a PC, you'll want to rename them to *.eml files, and then you'll be able to import them into various email programs like Thunderbird or Outlook; with some you'll need a utility, with others the import function is built in.
I haven't gotten far enough to determine if copying a backup of these folders onto a device restored from itunes backup will restore your archive of emails or not. Did I mention how annoying it is that Apple doesn't think your offline emails are worth saving when you do a backup of your device?
Best Answer
Currently on the iOS 8 app, this is not an available feature.