Lately the hotspot works quite stable for me on a fully up-to-date Byzantium L5.
The mobile data connection is less stable though, so maybe you do not have a mobile data connection. I recommend to install this package to see if you have an internet connection: network-manager-config-connectivity-pureos. An icon will be shown top left if there is no network connectivity.
To mitigate losing de mobile data connection, follow these instructions.
And here an older post regarding using the hotspot functionality on the L5.