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Out of interest do you get any type of error message when PC Suite is attempting to backup your Messages ? Also - give it some time to back up - I've left it for a good 20 minutes just to see whether it times out or comes back with any specific error message.
I experienced a similar issue and it was down to having to reinstall the MMS Sync component of PC Suite.
Two things I would try are :
1) As a previous poster recommended - just try backing up to the memory card to see whether this works OK or not. Not being able to do so would indicate it's not a PC Suite related issue and localised to the phone itself. 2) Try reinstall PC Suite functionality on the phone itself. With the N95 connected to your PC, load up PC Suite (the main program which gives an overview of all the applications that collectively comprise of PC Suite), then goto the Help Menu and choose "Reinstall PC Suite support on your phone" - then try backing up again.
If both of these steps fail, I'd recomend wiping your phone to a factory reset condition (although your memory card should NOT be affected if you follow the link below - but to be safe I'd take it out nevertheless !). The only problem with this solution is that it leaves you in the recursive problem of having to wipe a phone you want to take a backup of (!). Hopefully however, you won't have to do this ...
To reset your phone, follow the instructions in this link :