I heard in one of the religious discourses by some Sadhu that whenever Rama used to be in trouble during war with Ravna somehow Hanuman would come and save him. Some say that Lord Rama had recited Hanuman Kavach before fighting with Ravna and thus Lord Hanuman used to save him during sudden trouble. Is this true? Why Lord Rama being a supreme God needed recitation of Hanuman Kavacham?
No, Sri Rama never did any such thing. While there are many 'AdhyAtmika' versions of Ramayana in existence, the root of them all, and the historical report on which they are all based on, is the Valmiki Ramayana.
Valmiki Ramayana does not state any such hanumad kavacham being recited by Sri Rama (or any one for that matter) before fighting Ravana. In fact, the only prayer Sri Rama recited was the 'Aditya Hrydayam', which Sage Agastya came personally and imparted to him, before he fought Ravana a second & final time (the first time, Sri Rama decimated Ravana & his chariot so badly that he let Ravana escape, spend time in his palace in utter shame & re-equip himself to come back for his death).
The one & only instance of Hanuman ever 'saving' Sri Rama was when he was sent by Jambavaan to fetch medicinal herbs from Himalayas (Hanuman did that one before already but that was for saving Lakshmana if I remember correctly). That was it. And also, other than Indrajit, the only people Sri Rama actually fought in the war were Kumbhakarna & Ravana, both of whom he killed effortlessly.
This is NO slight on Hamunan's prowess btw. Per VAlmiki Ramayana, when Indrajit decimates the vAnanra army along with Sri Rama & Lakshmana & leaves the battlefield (or battle-sky rather since he always fought from sky), only 2 people were still left standing & in walk-able state. Those 2 were Vibheeshana & Hanuman. When they go waking others up & searching for Sri Rama & Lakshmana & they come across Jambavaan & wake him up, the first thing Jambavaan asks is not whether Sri Rama (or Lakshmana) is alive or not!! He actually asks Vibheeshana whether HanumAAn is alive or not! When Vibheeshana politely retorts him saying perhaps he meant to ask whether Sri Rama was alive or not, Jambavaan quips that no, he asked for HanumAAn because if Hanumaan was still alive, then there is hope for the entire army, but if Hanumaan was no longer alive, then the war was as good as over!!! That should tell you about the prowess of HanumAAn!
Jai Sri Rama, Jai HanumAAn!!