Here is a wild guess:
Looking in the zephyr api docs, it looks like the errorcode (-11) is EAGAIN.
Typically, in this just means that you should do it again!
The way i've been using EAGAIN is typically related to non-blocking I/O on sockets.
EAGAIN in this case means "No more data available right now, try again later".
So the error isn't a fatal error, rather a normal error (temporary condition) in such situations.
Given the logs that MQTT client is connected, perhaps this is just normal behaviour?
Can you confirm if there is an actual issue you are experiencing, like reconnections or packet drops or someting other than the fact that it's returning EAGAIN(-11)?
The documentation says that this mqtt_live function needs to be called periodically, within the keep alive time in order to keep a stable connection, thus EAGAIN would fit the description: "No need to do anything, call me later!"
there is another function called mqtt_ping, which says that "the use of the function is optional, as the library handles the connection keep-alive on it's own, see mqtt_live"