Wire & Telegram are both cloud connected, while Apps on the Signal protocol depend on your phone to be functioning and in reach AFAIK (huge annoyance/problem for me).
That's not true about Signal. You may probably be facing some bug that should be reported to the Signal team.
Telegram is completely cloud based. So all your conversations, except secret chats that are end-to-end encrypted, are stored on Telegram servers in plain text for as long as your account is active. This is why you can get a new device, activate it for your account and get all your conversations back on it from the Telegram servers.
Wire and Signal work differently. They use their servers as a temporary storage to hold your messages until the recipient comes online and then deliver them. Wire also retains the messages for a few days to allow delivery to multiple devices that a user may be using, with each device possibly coming online at different times. Signal doesn't have to support this because it's tied only to a single device, which is your phone.
