What is the Sharia ruling on continuing to invite female colleagues to wear the legitimate hijab, when they respond with promises or procrastination, which has caused the young man a bad psychological state?

One should abandon work environments with excessive and suspicious mixing, as it is a trial for one's faith. If it is not possible to leave the job, then extreme caution and lowering the gaze are obligatory, along with avoiding seclusion or contact with non-mahram women.

The one who invites to Allah must be patient, and not become annoyed or resentful of unpleasant situations, nor curse people unjustly.

Whoever is sincere in their call to Allah and adheres to the limits of the Sharia, Allah will reward them, even if no one follows them.