She learned of some faults in her fiancé and prayed istikhaarah about annulling the engagement, but it was not easy for her to do so
Question

I got engaged recently, but after the engagement I found out about some faults in my fiancé that I cannot put up with, and I felt that he is not suitable for me, in addition to the fact that he does not help me to obey Allah. Despite all that, every time I think of annulling the engagement and pray istikhaarah, asking Allah for guidance, something happens to make it difficult to annul it. What should I do? If I annul the engagement will I be disobeying Allah because my decision is something other than what He has chosen for me? Should I close my mind so that I will be obeying Allah?.
Praise be to Allah.If it has become clear to you that your fiancé has some faults that you cannot put up with, there is nothing wrong with annulling the engagement. This is better than getting married with the possibility of differences and conflicts, then divorce. 
If you have thought about that, then pray istikhaarah and ask Allah for guidance, then tell your wali so that he can apologize to your fiancé. Thus your engagement will be annulled. 
Istikhaarah does not mean that you should close your mind, and it is not only focused on material matters that surround man, rather it is complementary to that. A person may be hesitant about some matter, because it involves both good and bad, pros and cons, or because he is uncertain of the consequences, so he asks Allah to make easy for him the good that He knows. 
It may seem to you that a suitor is free of faults, but Allah knows that he is not suitable for you and that there are faults in him of which you are unaware, or that you are not suitable for him. Or it may seem to you that there are faults in a suitor, but Allah knows that he is suitable for you and that his faults will disappear, or that they are not actually faults, or that he is suitable for this woman, and other unseen matters that no one knows except Allah, may He be glorified. 
It is well known that no one can succeed except with the help and guidance of Allah, and that if he were to be left to his own devices he would be an utter loser. So if you have prayed istikhaarah, asking Allah for guidance, about something, then go ahead with it. If it is good, Allah will make it easy and facilitate it, and if it is bad, Allah will divert you from it or divert it from you. 
To apply this to your question: because of the faults that you see in your fiancé, you should pray istikhaarah and ask Allah for guidance about annulling the engagement, and go ahead with it, by speaking to your wali or to someone who will convey news of the annulment of the engagement. If the matter comes to an end and is made easy, that is better for you, in sha Allah. If it becomes difficult to annul the engagement, then there is nothing good for you in that now; it may be that Allah knows that your getting married to him is better for you, or that continuing the engagement for a while longer is better for you. There is no reason why you should not repeat istikhaarah several times. 
We should point out a number of things: 
1.Istikhaarah is not to be used concerning things that are obligatory or forbidden or makrooh, except when the hesitation is about setting a time to do an obligatory action. Based on that, if it has become apparent that your fiancé does not pray or that he commits immoral actions, for example, then you must refuse him, and it is not prescribed to pray istikhaarah in that case.
2.The issue of things being made easy or difficult may involve some doubt and waswasah (whispers from the shaytaan). Perhaps the wali will try to contact the fiancé to tell him of the annulment and will not be able to get in touch with him, so it is said that the matter has become difficult. But that is not the case. Rather he should try again to get in touch with him, or send someone to tell him the news, and so on.
3.If a person goes against what is indicated by istikhaarah, he is not disobeying Allah or sinning, but he will miss out on much goodness and will regret it if he does not do it, or harm may befall him if he goes ahead with something that Allah has not made easy for him. Perfect faith and trust in Allah means delegating one’s affairs to Allah and accepting His decision, and going ahead with the matter after praying istikhaarah and deciding upon a course of action, and not paying attention to waswasah.
Please see also the answers to questions no. 11981 and 5882. 
We ask Allah to make good easy for you wherever it may be. 
And Allah knows best.