That prayer is the original Arabic of the Bab's "Is there any Remover of Difficulties". I've heard the 360 thing as well, but really, I couldn't tell you - I've heard the same thing with an even greater number of invocations of "Ya Ala al-Mustagath".
I have also heard of traditions where Halman Mofarrajen is recited up to 500 times. The following guidance is from the Universal House of Justice on the matter:
"On page 1 of your October News letter you have quoted the Bab's prayer for the removal of difficulties and have added: 'Baha'u'llah has said to repeat this prayer 500 times by day and by night that it may aid us to recognize Him and our souls will be illumined.'
"The above statement gives the impression that the repetition of the said prayer 500 times is one of the prescribed devotionals of the Faith, and has a specified effect on the believer who observes this form of prayer.
"We do not feel it is justified to infer such conclusions from the reference in 'God Passes By', page 119, which you mention. The passage in question obviously refers to a specific circumstance in the life of Baha'u'llah in Baghdad before the declaration of His Mission, and should not be presented to the believers as one of the prescribed observances of the faith."
(From a letter of the Universal House of Justice to a National Spiritual Assembly, November 24, 1971; quoted in Lights of Guidance, no. 1528, p. 466))
`Bid them recite: "Is there any Remover of difficulties save God? Say: Praised be God! He is God! All are His servants, and all abide by His bidding!" Tell them to repeat it five hundred times, nay, a thousand times, by day and by night, sleeping and waking, that haply the Countenance of Glory may be unveiled to their eyes, and tiers of light descend upon them.'
(Shoghi Effendi citing Nabíl citing Bahá'u'lláh in God Passes By, p. 119)