The continuance of supplication in distress and ease was mentioned in the islamic texts. God’s messenger (pbuh) says:” Remember God in ease to remember you in distress”. 
Abu Abdullah Al Sadeq (a.s) says:” He who precedes supplication is answered in time of distress where angels say: this voice is known and his supplication is not to be prevented from reaching the sky. But he who doesn't precede supplication, isn’t answered in time distress where say:” we don't know this voice”. 
Abu Abdullah Al Sadeq (a.s) says:” Supplication in ease makes requests for needs answered in time of distress”.
Abu Abdullah Al Sadeq (a.s) says:” He who wants his supplication to be answered in time of distress should supplicate in time of ease”. 
"My grandfather used to say: precede supplication because when a servant supplicates in time of distress angels at that time say: this voice is known.
But if he doesn’t supplicate, angels say in times of distress: where were you before today?”. 
These texts indicate a beautiful and precise meaning. Supplication is a sincere approach of a servant towards God and the most fulfilled supplication is the most sincere to God.
So if the approach takes place with heart attendance and a servant is completely directed towards God, nothing prevents supplication from being answered. But if sincerity is weak, the answer of supplication is in its same level of weakness. Approaching God and making a heart present in the hands of Him is achieved with lots of supplication.
This happens to a man by his many supplications, same as any other action that he does. The more a man supplicates, he is more able to approach God almighty and the more his heart is directed towards Him.
So if misfortunes surprise him and he moves towards God, his heart will be directed towards God quickly and easily. His supplication will be closer to be answered and nothing prevents response at that time.
It was narrated by Abu Al Fadel bin Al Abbas:'' God's messenger (pbuh) told me: Observe God's orders, and he shall guard you. Herd His call and He shall be with you. Hear his call in ease and He shall be with you in distress”. 
Ali bin Al Hussein says:” I didn’t see an importance as that of preceding supplication since a servant’s supplication isn’t answered any time”. 
Abu Zarr (may God bestow him with His mercy) says:” God’s messenger says: O Aba Zarr, hear God’s call in ease and he shall be with you in distress, and when you seek aid, seek only God’s aid”. 
It was narrated that Abu Jaafar (a.s) says:” a believer’s supplication in the time of ease should be the same as his supplication in the time of distress. He shouldn’t calm down in times of distress. So don’t feel bored of supplication because it has a great importance in the eyes of God almighty”. 
Supplication of Ahl Al Bayt (peace be upon them), Al Sheikh Mohammad Mahdi Al Asfi
 The Shiite Means 4: 1097, part 8672
 Al Shiite Means 8: 1096, part 866
 Al Shiite Means 4: 1096, part 8665
 Al Shiite Means 4: 1096, part 8660
 Al Shiite Means 4: 1096, part 8667
 Man La Yahduruhu Al Faqih 2: 358
 Kitab Al Irshad for Al Sheikh Al Mufed: 277
 Al Shiite Means 4: 1098, The Supplicator’s Tools for Ibn Fahed Al Huliy: 127
 Al Shiite Means 4: 1111, part 8729.