I have a 2010 Ecomotive with Media System 2.1 bluetooth, the same phone (iPhone 4S) and suffer the same problems as you describe.
I have my phone in a holder (I use a Brodit Pro-clip), so I can see the screen while driving. When it "doesn't ring", the phone itself is actually ringing (obviously), but because the audio is routed via the car - which doesn't detect the incoming call - you can't tell audibly that the phone is ringing and you can't answer the call (unless you physically pick up the handset, which is obviously not advisable!).
I've yet to find a foolproof solution that I'm happy with, but I have discovered a workaround of sorts:
After getting starting the car and waiting for your phone to pair as usual, go into the phone settings and disable Bluetooth (Settings > General > Bluetooth > Off). The car will display that the phone has disconnected. Then enable it again, wait for the "SEAT..." device to show up again on the phone and click the device (not the '>' symbol!) to re-connect to the car. The car will acknowledge the phone connected and start loading the contact lists etc as usual.
I find that by initiating the connection from the phone in this way, I am able to properly receive calls more of the time - I have no idea why.
Unfortunately, these niggles are virtually impossible to get resolved. In all cases, the makers of each device will claim the fault lies with the other device.
If you ask SEAT, they'll tell you it's your phone and if you ask Apple, they'll tell you it's the car... it's the standard response to all these problems I'm afraid - it's infuriating, but they all do it.
Trying to get your
problem escalated to someone sufficiently technical to actually know what might be wrong (apart from pointing you to the existing useless documentation) is virtually impossible!