All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.
After extensive research, we have not come across a Thikr that would give protection for a long period of time, like a week or a month. But there are authentic narrations about Athkaar that protect from devils for one day or three days.
An-Nu'maan ibn Basheer narrated that the Prophet said, "Verily, Allah wrote a book two thousand years before He created the heavens and the earth; from it, He sent down two verses with which He concluded Soorah Al-Baqarah. The devil cannot approach a house in which they are recited for three nights." [At-Tirmithi, Al-Haakim, At-Tabaraani. Al-Haythami said, "The narrators of this hadeeth are trustworthy." Al-Albaani graded it Saheeh (sound)]
In Saheeh Ibn Hibbaan, it was reported that Sahl ibn Sa‘d narrated that the Prophet said, "For everything, there is a hump (pinnacle), and the hump of the Quran is Soorah Al-Baqarah; whoever recites it by night in his house, the devil will not enter it for three nights, and whoever recites it by day, the devil will not enter his house for three days." [Al-Albaani graded it Hasan (good)]
Among the Thikr that gives protection throughout the day, from morning to evening or from evening to morning, is the confirmed report from Abu Hurayrah wherein he related that the Prophet said:
"Whoever says, 'La Ilaaha Illa Allah Wahdahu La Shareeka Lahu Lahul Mulku Wa Lahul Hamdu Wa Huwa ‘Ala Kulli Shay'in Qadeer' (There is nothing worthy of worship except Allah alone with no partner; His is the dominion, and to Him be praise, and He has power over all things.) one hundred times in a day, it is as if he had freed ten slaves; he gets one hundred rewards, and one hundred of his sins are wiped out; and it (this Thikr) becomes a protection for him from the devil all that day until the evening, and nobody will do anything better than what he did except someone who did more than him." [Al-Bukhaari and Muslim]
Moreover, in the story of Abu Hurayrah when he was appointed to guard the zakaah (obligatory charity) of Ramadan, he (the devil) said, "When you go to your bed, recite the verse of Al-Kursi [Quran 2:255], and there will be a guard from Allah with you all night long, and no devil will be able to come near you till morning." Thereupon, the Prophet said, "He said the truth while he is a liar. That was a devil." [Al-Bukhaari]
The Prophet also said:
"Whoever recites three times in the evening, 'Bismillah-illathi la yadhurru ma'a ismihi shai'un fil-ardhi wa la fis-samaa'i wa Huwa as-Samee‘ul-‘Aleem' (In the Name of Allah with Whose Name nothing in the earth or in the heaven can cause harm, and He is the All-Hearing and All-Knowing.) will not suffer a sudden affliction until the morning. And whoever says it three times in the morning will not suffer a sudden affliction until the evening." In another narration: "nothing will harm him." [Abu Daawood, At- Tirmithi, Ibn Maajah, and Ahmad]
Abu Hurayrah further narrated that the Prophet said, "Whoever says three times in the evening, 'A‘oothu bikalimaat-illaahi at-taammaati min sharri ma khalaq' (I seek refuge in Allah’s Perfect Words from the evil of what he created.), no poisonous sting shall harm him that night."
Allah knows best.