> And what if the transaction does take place, but the record is lost?
The design of the blockchain prevents that.
When you create a transaction, you are saying send X amount of bitcoins from address A to address B. You sign it with your private key to address A, proving they were yours to send. It then gets broadcast to the network of 6000 nodes, each of which compares your transaction to the balance of address A, to verify you had enough to send. They also validate your signature and some other technical checks. If it passes, they add it to their pool of pending transactions. So at this point the transaction is stored in 6000 places.
Miners are also nodes, and see the transaction. They compete to find a "hash" (checksum) for a block of transactions, in order to win the block reward (currently 25 new bitcoins worth almost $10,000) plus transaction fees from the included transactions. Blocks also record the hash of the previous block, linking them in a chain (hence "blockchain"). When your transaction is included in a block, it is "confirmed", and removed by the network nodes from the pool of pending transactions. The new block is added to their copy of the growing blockchain. The transaction is still stored in 6000 places, but in the chain instead of the pending pool.
At no point can the record of the transaction be "lost", it's in too many places. It can remain pending if blocks are full and it never gets into one. If the pool of pending transactions gets too large, nodes can start dropping some to save memory space. In that case, your transaction was never completed. You can try again later, since the official blockchain shows you still have the funds in address A.
The current block size limit is 1 Megabyte, which allows about 2500 transactions per block, and blocks average one per 10 minutes. In theory that allows 360,000 per day, and lately there have been 220,000 per day getting processed. The argument is over how to increase capacity, since we are getting close to it. The simple answer is to raise the size limit, but that increases bandwidth, block transmission time, storage requirements, etc. An alternative is to move parts of transactions (the signatures) or entire swathes of transactions (side chains and such) off the main bitcoin chain, and only record the important bits. For example "this transaction on the main chain summarizes 1,024 smaller transactions on side chain Z".
Everyone involved wants bitcoin to grow, and it is obvious capacity needs to increase. They disagree on *how* to do it.