The 510 was sold in 2008, so yes, I'd say "several years old". Eons, in GPS-map-years.
Let's take this from the top.
1) "...ever since it was new..." What map version DO you have on your unit now? Did you ever take advantage of the free one-time update to the map version that was on your device when you received it? It is possible that a map was released between the time your unit was built and the time you purchased and first started using it, hence "ever since" unless you did take advantage of that offer.
2) "...it says that the map is out of date..."
You're seeing this on the device, or is Home saying this? Perhaps both?
If you are talking about Mapshare updates, those are incremental. The base map itself may well be quite out of date. That's why they sell updated maps.
3) "...yet the TT website says that my device is updated..."
That may well be true. Your base map may be quite out of date, but at least it has the most recent Mapshare patches applied, which helps.
Mapshare does NOT cover all of the possible changes that occur when new maps are released. So you can be 'current' on Mapshare updates, but the base geometry included in the map may become out of date. Not all changes to maps can be sent and incorporated in Mapshare updates.