Someone who's been denied eligibility for Medicaidcan reapply anytime he has a change in circumstances. So, as soon as some of your brother's assets are sold, he can reapply. (You should check with the local Medicaid office where he previously applied, just to make sure they don't have any additional local rules, such as a 30-day waiting period.) There is no penalty for reapplying, and if the application is successful, coverage can date back to the date of applying.
Also, you should double-check the asset limit. In every state -- including Arkansas, according to its own state Medicaid Web site -- the $2,000 asset limit does NOT include the applicant's car, up to a certain value ($4,500 in Arkansas). So, you may not need to sell his car in order for him to qualify.
Remember, too, that after he has been receiving Social Security disability benefits for 24 months, he will be eligible for full Medicare coverage (in addition to Medicaid if he's eligible for that coverage, too).