Does the family's rejection of the suitor due to his prior arrest indicate the result of Istikhara that the marriage should not be completed, or should the suitor try again to get the girl out of her environment, and at what point does the suitor know that there is no good in the matter and stop trying?

There is no objection to renewing the marriage proposal. Istikhara (definition) is seeking Allah's choice for the better of two matters, so take the necessary measures, then be content with Allah's decree. If the family prevents the girl from marrying, she may refer her case to the judiciary. However, it is preferable to try and convince them or to seek the mediation of respected individuals. Be keen on the girl as long as she possesses religiosity and good character. If the matter becomes too difficult, then turn away from her, for Allah knows best what is good.