Is refraining from supplication and seeking a necessary and important need that has not yet been fulfilled considered a sin?

There is no obligation to supplicate for a specific worldly matter, nor is there any sin in not supplicating for it. What is blameworthy is for a servant to abandon supplication out of haste or impatience for a response. A response does not necessarily mean giving exactly what was asked for or at the specified time; rather, it occurs in one of three ways: expediting the request, storing it for the hereafter, or averting an equivalent evil.

Conditions must be met by the supplicant, such as knowing that there is no power except with Allah, having sincere intention, being present of heart, avoiding unlawful earnings, and not despairing of a response. Conditions also apply to what is supplicated for: it must be permissible Islamically, involve no sin, and not entail severing ties of kinship.

Thus, an answered supplication either grants the requested item, or something similar, or wards off evil, or stores it for the Day of Judgment, and it is all bound by Allah's will.

It is recommended to continue supplicating and to be persistent, while asking Allah for what is best in worldly matters. If Allah grants you something, ask Him to make it a means of assisting you in obeying Him.