Must my wallet be connected to the internet to receive payments? (This question applies to private wallets, stored in a local computer. Not so much for online wallets, which are supposed to always be connected to the internet) 

Let's say I have a wallet with several addresses. Somebody (maybe even myself) makes a transfer to one of my addresses. My impression is that my bitcoin client (the one managing the wallet to which the address is associated) must be running and connected to the internet in order for this transfer to be executed.

I say this because, since a wallet has real money, the bitcoins (those unique bitcoins that have been transferred) must arrive to the wallet somehow. But if my wallet is not connected, this is impossible.

So here my questions:


what happens if the wallet is not connected to the internet? Where are the bitcoins? Are they in a "bitcoin limbo" until they are transferred to my wallet? 
How is this managed from the blockchain point of view? Are transfers marked as "done" when the money has been transferred to a wallet?
is there any kind of timeout? What happens if I do not connect my client for a day / month / year / ever? Are the bitcoins lost, or is the transfer cancelled?


Maybe I am misunderstanding what an address / wallet really represents.
No, the transactions are weaved into the blockchain by the p2p network of miners. That's what counts. Your address is only a keypair that proves you ownership. The concept of cold storage is exactly the idea to not connect to the internet so nobody can steal your coins (or rather, the key to access your wallet).