Yes -- Saito is the first "transient blockchain" and everything will technically fall off the network eventually unless someone acts to preserve it.
It is possible to maintain data on-chain, although in most cases the users sending transactions and the users receiving transactions will not want to pay for that and will prefer bear the burden of archiving them. There is no reason for the entire network to backup my email inbox, for instance. So "permanent storage" will only really be needed for tokens that represent monetary value.
We do have two ways to maintain data on-chain in perpetuity though:
1. applications can manually rebroadcast transactions whenever they near the end of the chain. This is dirt-cheap and helps preserve the security of the network for complicated reasons that you can read up about in our explanation of how Proof-of-Transactions / Proof-of-Relay works.
2. nodes creating new blocks are forced to rebroadcast transactions that meet consensus/code-level criteria qualifying for rebroadcasting (i.e. their "rebroadcast" flag is set and they have enough money to pay for it. We intend this as a fallback rather than the main mechanism -- it will be more expensive.
Generally though, shifting to a transient chain is important as it is one of the steps needed to "fix" the economics of existing consensus mechanisms. It allows us to price the cost of storing a transaction forever by dividing infinity up into manageable chunks during each of which storage costs are accurate and market-driven and fees are handed over to the nodes that are actually doing the work in that point at time.