Earlier quoted context omitted.
Surely battery saving modes should not drop messages? It could delay them but should never (well, almost never) drop them.
With no knowledge of how signal's servers actually implement this, I would like to ask you... how long should the central server hold on to the (encrypted) message that Alice sends to Bob if Bob never becomes available again?
(But perhaps a new protocol could take the opportunity to improve things further and offer on-line delivery status notifications throughout the process.)
No matter what, messages should never be silently dropped.