Disconnect events with rate-limited publishes

I have deployed a device with a code that often happens to publish more than 1 event per second - my bad I am getting rate-limited publishes warning.
On top of that I face disconnect events - but last report states signal quality to bee good.
Is it possible that my device is publishing too much - so it gets disconnected from cellular network?

The prototype is deployed in a remote location - how can I force OTA update to push to it a firmware with publish rate fix?