Wa`alykum as-Salamu wa Rahmatullahi wa Barakaatuh.
Resolving is making a firm intention. It is not the same as a vow. A vow is a solemn oath one makes by invoking the name of Allah. If one were to break a solemn oath, one should expiate for it by feeding ten poor persons or fasting three days.
In the case of repentance, one should form a sincere intention to refrain from the sin. If one were to repeat the same, he should make repentance again. However, by persisting on the sin, one may fall in the category of those who are jesting, which is blasphemous and is a greater sin.
After all, he would be risking his eternal salvation if he were to die in such a state. Therefore, as believers, we ought to persist in repentance by keeping away from sins. One should implore the mercy and help of Allah for doing so. With sincere intention, coupled with the grace of Allah, one can hope to achieve success.
Allah Almighty knows best.
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