This happens when you backup to a non-apple device.. actually a TC in particular is the only apple supported network device for TM.
Did you try a reboot of the whole network.. and you can verify the backups .. see A5 in pondiini.
The same thing happens even on a USB drive plugged into an Airport Extreme. It can work fine for ages and then just suddenly refuses to connect.
Did this happen when you updated to 10.8.3.. does the date of the last backup correspond to the update? It would not surprise me if they did some little tweak that took out your non-authorised backup method.
Now I have not tried it but lots of these issues started with Lion when the security level in AFP was changed. Security for a file protocol is irrelevant on your local network so really only relevant to using BTMM and iCloud.. which was also introduced with Lion.. that is when everything went to pot.
I would look at the Synology as running better at the older level of security and making the adjustments required on your computer.
I have a NAS and I have the same issue happen a couple of times. I am still using Snow Leopard though so the above suggestion is not a cure all.. I think you just have to accept that Apple builds a walled garden.. if you try and step out of the garden.. anything over the wall.. can be expected to behave badly on occasions. Set up another folder on the synology and start a new TM backup. Or use CCC or superduper etc..
It is standard error for TM.. stupid thing.. sorry.. you need to eject the sparsebundle...
See C12 here for more info.
Try just rebooting the Synology.. I thought it was a TC fault more than a Mac fault.. but there you go.