Howitzers were to fire grenades or grapeshot. It would have been hard to find cannon balls with a matching calibre.
You will find some Prussian data on firing rates and moving speeds at the link below.
Firing at maximum speed by exchanging exhausted gunners maybe could go on for 1 hour, but the gun tube would heat up with the time and I don't know whether this was considered dangerous or not. Practising with replica flintlock muskets and blackpowder, we proved that even if the barrel has become too hot to touch it, tts temperatur will still be far from being able to ignite the blackpowder by contact.
Also, concentration on firing speed would have a negative affect on the cost of accuracy in aiming.
Which actual circumstances were you thinking of, when posing your question ?