If you want to follow up on performance tuning Modbus (which can impact other sub-systems, it’s very capable of generating buckets of Item updates) see
For the MQTT stuff, you’ve got something of a job to pin it down further.
There’s no suggestion that the link between openHAB and your broker is in trouble, the clues say it remains alive.
(Where is your broker living? Which one is it?)
It looks like either
Broker has ‘forgotten’ OH subscriptions, or lost pathway to push them.
or
openHAB is forgetting to process them, maybe because it has forgotten channels with matching topics.
Neither are known problems.
I think you might need to be debug logging io.mqtt.transport or something to see incoming topic messages .