iPhones do not autonomously delete all (or any) messages, so I'm afraid its either your doing or that of someone who's had access to your phone (friends, kids, partner).
Some of the messages are irreplaceable
and
the last backup I made, (which was unfortunately done quite a while ago)
Hmm..... it never ceases to amaze me how people keep files/documents/messages on their electronic devices that they consider "irreplaceable" and yet can't be bothered to implement a regular backup routine. I'm afraid its something that gets no tea and sympathy from me ...
IF IT IS IMPORTANT TO YOU, BACK IT UP ON A REGULAR BASIS TO RELIABLE STORAGE ! (preferably three independent recent copies stored on independent reliable devices (no USB sticks or that sort of rubbish) if its
really important to you)..... its something I repeat time and time again on here !
Infact since you can even set an iPhone to backup seamlessly to Apple iCloud there is absolutely zero excuse for not being able to do regular backups.... since the iCloud method is fully automated whenever you're on WiFi, no need to remember to plug in USB cables, all you need to do is make sure it's backing up ok.
The problem I have, is that iTunes is set to autosync
You can turn it off.
it will automatically take what is on the phone, and rewrite what is on the computer with it, thus I will lose my messages forever.
By the sounds of your description so far, its highly likely that you've lost your messages forever anyway...
If you do a restore, then yes, it will re-image your phone with the contents of your last backup... the fact your last backup is of a certain vintage is not my or Apple's problem (not that this problem is anything to do with Apple in the first place).
I'm afraid you're probably going to find you've just learnt about the importance of backups... the hard way.